MPMP: Can you play Scrabble over a video call?

You can enter the submittable part of the puzzle at www.think-maths.co.uk/maths-p...
Everything about Vicki is on her website: www.vickipipe.co.uk/
Or go straight to the All The Stations channel!
/ @allthestations
Get your own random quantum-noise numbers here: qrng.anu.edu.au/
These are my scrabble numbers. I have not double checked them, so please let me know if you do.
Ten million simulations:
Fixed points: 5.9604827
Alphabetical neighbours: 6.6008077
Pairs: 4.3016657
Triples: 0.2712588
Fours: 0.0184608
Fives: 0.0012537
Just two rounds of random shunting:
Fixed points: 5.9601175
Alphabetical neighbours: 5.6288508
Pairs: 6.263659
Triples: 0.4552404
Fours: 0.0385577
Fives: 0.0033718
Two random shunts and a 2-2-3-3 shuffle:
Fixed points: 5.9590569
Alphabetical neighbours: 7.2059461
Pairs: 4.2509397
Triples: 0.3174862
Fours: 0.0272161
Fives: 0.0023192
Three random shunts and a 2-2-3-3 shuffle:
Fixed points: 5.9611759
Alphabetical neighbours: 6.6348292
Pairs: 4.2771024
Triples: 0.2715075
Fours: 0.0184781
Fives: 0.0012264
Here is the submittable puzzle again with the letter values:
How many ways, from the 100 standard scrabble tiles, can you choose seven which total 46 points? Clarification: for this we mean distinct scrabble hands (groups of 7 letters), so order does not matter and identical letters are indistinguishable.
9 × A worth 1 point
2 × B worth 3 points
2 × C worth 3 points
4 × D worth 2 points
12 × E worth 1 point
2 × F worth 4 points
3 × G worth 2 points
2 × H worth 4 points
9 × I worth 1 point
1 × J worth 8 points
1 × K worth 5 points
4 × L worth 1 point
2 × M worth 3 points
6 × N worth 1 point
8 × O worth 1 point
2 × P worth 3 points
1 × Q worth 10 points
6 × R worth 1 point
4 × S worth 1 point
6 × T worth 1 point
4 × U worth 1 point
2 × V worth 4 points
2 × W worth 4 points
1 × X worth 8 points
2 × Y worth 4 points
1 × Z worth 10 points
2 × _ worth 0 points
Thanks as always to my principle channel sponsor Jane Street!
CORRECTIONS
- Nothing yet. Let me know if you spot anything!
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Bevan Timm
Steve Davidson
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Filming and editing by Matt Parker
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
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Ok, here is your hint: see if you can work out how many ways you can get a total of 48 points (there should be 50). Then try 46 points.

[@matthewellisor5835]

...And that's how the Parker Shuffle was defeated by a square of squares.

[@LegendarySkar]

The Parker squared Square Shuffle

[@DenisRyan]

Came here to say similar. Well played.

[@yvesisnotaname2813]

Denis Ryan The Parker Square Shuffle

[@ykl1277]

Parker^2 shuffle

[@feronanthus9756]

Defeated or proved?

[@TC-mb2pw]

One person has the bag - takes out random tiles for the other person on their turn but shows them only to the camera so they can't see them themselves. Not maths, but a lot easier!

[@bbgun061]

When all you have is a hammer, everything looks like a nail. Of course the mathematician is going to find a mathematical solution...

[@Tondadrd]

I agree. They said over a phone, but if the phone is smart, you can video call.

[@user-ow1bc4sx2r]

This is a much better solution hahahah

[@mattsnyder4754]

Vedant Parekh ummm.... and I quote “and shows them only to the camera so they can’t see them themselves.”

[@dan200smx7]

@@vedant519 not if they don't cheat and only show the camera, which is assumed (obviously you don't show your own)

[@josephrissler9847]

If you add 21 extra "marker" tiles that are distinct while facedown, you can add a whole new column and row, and use the markers to determine if the shuffle is correct. It would also help you in teaching another person how to do the shuffle because they can see your marker tiles.

[@MateusSFigueiredo]

That's a great idea! But I don't know how that would work with the actual set. You can't just make new tiles in the real set. Maybe burn a few letters and keep them face up.

[@josephrissler9847]

@@MateusSFigueiredo you wouldn't need the tiles to match the set, though it's probably easier for handling if sacrifice another set and write numbers on the back. I was thinking you could just make your own tiles like Matt did for the markers.

[@Skatche]

It's a good idea, but it has the drawback of needing a sequence of base-eleven digits rather than base-ten digits.

[@maxonmendel5757]

@@Skatche why's that?

[@_adela]

​@@maxonmendel5757 You would need 11x11 grid for 121 tiles and since they used decimals of a random number, you would never shift the tiles by 10, since decimals are 0-9, which would create bias. You could, of course, just do floor(11 x Random) 11 times and tell each number to the other player.

[@Yaksavin]

The obvious way to play is with quantum entangled scrabble pieces

[@RFC3514]

If you break a B in half, does that give you two entangled Ds?

[@andrewsparkes8829]

@@RFC3514 Lots of average-breasted women wish so.

[@RFC3514]

If they're entangled, size won't save them.

The Parker Shuffle?

[@dan200smx7]

The 10x10 Parker square?

[@TheDannyHamilton]

When you give shuffling a go, but fall just a bit short.

[@davidmulqueen8322]

The Enoch Root shuffle.

[@armofrobot]

That sounds like the new mathematical dance craze!

[@MathTchr101]

I came here to make a Parker Square comment and I'm glad I'm not the first. XD

[@carnaedy]

Easy, just play "Duplicate Scrabble". All players are playing the same hand (you can easily accommodate much more than two people!). After some fixed time, all of them reveal the word that they come up with and score appropriately. Then the best scoring word is put on the board to establish the new situation, tiles in hand are replenished (only one person does that and notifies others what the new tiles are), and the cycle repeats. The players always have the same hand and play the same board situation, so it's a fair game. Obviously, the person with the best score at the end of the game wins.

[@namenamington]

I think you just (re-)invented Countdown.

[@cyrylo23]

duplicate Scrabble has a bit different strategy than standard Scrabble. In standard scrabble it might be worth to hold on blanks and some characters to place all 7 tiles later to earn bonus.

[@carnaedy]

@@cyrylo23 That's a very valid point, thanks.

[@ink7761]

This is countdown

[@harrybarrow6222]

Paulina Jonušaitė Assuming two competent players, what do you do if they both produce the same word?

[@cpsof]

Poker tournament: "Shuffle up..." *15 minutes later* "...and deal!"

[@daminox]

He actually did a video awhile ago about how to play poker over the mail.

[@michelfug]

Parker poker

[@Kram1032]

Porker Paker

[@frederickm9823]

MPMP should be written as (MP)^2, so we can have another Parker Square 🤔

[@gruber3349]

Shoutouts to Germany ;)

[@frederickm9823]

@@gruber3349 Haha, thank you. Didn't realize auto correct was changing my words 😅

[@asailijhijr]

But the MPs aren't interacting multiplicatively, they're additive or set-restrictive. So 2(MP) would be more correct. Or (MP) subscript 2 like chemistry notation.

[@frederickm9823]

@@asailijhijr (MP)^2 = MP*MP = MPMP :)

[@shaileshrana7165]

Didn't we get a Parker Square at 14:16?

[@olliejenner]

Hey Matt! - I'm a competitive scrabble player - Cool to see you tackling an interesting problem like this. There's a few issues (outside of what you ran into). You need to handle exchanges that happen in game, throwing back vowel-heavy or consonant-heavy racks or un-useful tiles (the Q in particular). Not sure of the best method to "shuffle" the exchanged tiles back into the "bag" particularly if it happens late in the game (called a "Q Bomb" if you swap it with the goal of getting the other player to pick it up when it's useless). There's a scrabble variant I've heard of called snake scrabble where the tiles are put in a random order and one player draws from one end and another player draws from the other end. The idea being 2 different pairs of players can play the "same" game of scrabble (eg if I'm playing you and Vicki is playing Geoff, I'd have the same racks as Geoff and you'd have the same racks as Vicki). This is a little similar. The best solution (as mentioned in the vid) is probably a 3rd party (person or software) telling each player what they draw. I think the method that was used in postal scrabble was to just play open-handed (removing the hidden info). My best attempt at a quality of life improvement for the shuffling process would be to start with a random position (one player draws the 100 tiles and the other player copies it) so it starts as a "random" but known 10x10 grid - this gets rid of the need to do enough shufflling to split the runs of the same letter up, we just need to do enough make the players unable to track where the tiles are. This is pretty hard - I'm reasonably confident I could track the power tiles (QXKJZSSSS and two blanks) through lots of different processes. I thought repeated swaps of two tiles in the grid (eg swap R1C5 with R7C8) would be easy to do quickly and lots of repetitions and less likely to desynchronise the two people's grids. I wonder if there are more sopisticated shuffling operations on the grid that are easy to do, but hard to track - Like designing a maze that you yourself then have to solve. Cheers for the video - I welcome as much Scrabble content as I can get! Shoutout to Tom Crosbie who did a Scrabble tile grid magic trick in his Edinburgh show last year.

[@klutterkicker]

Time playing scrabble: 60 minutes. Time shuffling Scrabble pieces: 90 minutes. Using encrypted communication by hand: timeless.

[@mattsnyder4754]

Alternate solution. Find a third friend who acts as the “moderator.” They draw tiles and show them to the appropriate persons, and manage the game board

[@stumbling]

Having a whole two friends is a bit of a tall order.

[@coolfred9083]

But what if everyone else has died from the coronavirus and you really need to play scrabble?

[@joostvanrens]

@@stumbling they don't necessarily need to be whole to be a moderator

[@user-vn7ce5ig1z]

[sic]> Having a whole two friends is a bit of a tall order. What if your friends aren't whole but are rational? 🤔

[@mattsnyder4754]

- that’s fine. As long as they aren’t irrational or imaginary.

[@coryman125]

The real challenge here: knowing the initial state and final state of both boards, figure out what went wrong ;)

[@yoavshati]

Vicki: *reveals the letters N and O* *starts saying "no" a lot* Matt: *briefly shows the letters O and K* *immidiately says "ok"*

[@WMTeWu]

Is that contagious? Oh wait.... never mind!

[@matthewellisor5835]

@@WMTeWu Too soon

[@RecursiveTriforce]

I'm sorry to disappoint you but he showed "A" and "K"

[@bloergk]

In welsh Scrabble, every letter is worth 1 point except for "E" which is worth 10

[@jackdog06]

bloergk the “y” actually subtracts points

[@leeprice133]

Sorry to be that guy, but 'E' is the 5th most common letter in Welsh ;)

[@leeprice133]

@@rosiefay7283 Ch and Ff as well

[@JNCressey]

@@rosiefay7283, is LL a single tile? are you allowed to make it up with two L tiles?

[@qwertyTRiG]

@@JNCressey LL, FF, DD, and CH are digraphs in Welsh.

[@Cliff86]

A Parker Square of Scrabble tiles shuffled to perfection

[@nanamacapagal8342]

Perfection.

[@nanigopalsaha2408]

I see that you're a man of culture as well.

[@asailijhijr]

> Parker Square @@nanamacapagal8342

[@Tefans97]

MPMP II the revenge of the squares

[@nanamacapagal8342]

@@asailijhijr oh right... The Parker Square is never perfect

[@jackdog06]

“We could download an app, but that would be even less social” “What if we made a program to play scrabble for us?” ...wait...

[@NotOnTask]

This might just be a joke, but if not: I think for the second program they just wanted a program to draw the letters for them, but they would still be playing the tiles physically.

[@daminox]

i'm not sure why they wouldn't just play over an app WHILE having a video conference call.

[@bluerizlagirl]

You could both download the developer kit, open up a GitHub and develop your own app together. If you're into that sort of stuff .....

[@happy_labs]

@@daminox Yeah, jokes aside this is what I've been doing with friends and it works really well. If you have a laptop/tablet for the video call and a phone to play the game you can talk and play at the same time. I've been playing poker with friends and it's great

[@Gihntemos]

We should really just give them Tabletop Simulator at this point, lol.

[@Iojeka]

I was going to comment the same thing! Been playing board games there instead of my spare room lately

[@georgelionon9050]

You could also simply give both a pseudo random number generated mini program, that tells them what letters to take into their hand, while not knowing what the other person gets (as long they don't change the program to tell them)

[@Godishus]

I'd say those two boards were very well shuffled. They looked nothing alike! :)

[@TheAnimatorsUnite]

Ah, but you can see sequences where they are the same, like the "PRNA" but the next letter "i" was replaced to the front on one of the boards. I am thinking they only screwed up near the end.

@@TheAnimatorsUnite Yep, I noticed several same sequences in both top and bottom row (didn't check others).

[@RoderickEtheria]

Actually, they do look alike. Note the letters in each of the bottom rows. There not exactly in the same order, but they do have the same letters in the same rows. The mistake was based on the fact the rows were not shifted the same amount with the randomized numbers. The columns were shifted the same amount, which is why the letters are the same in each row, but the columns are wrong, which is caused by not shifting the rows the same amount.

[@JohnBrennanRhodes]

Great video! I worked out where the difference in their tiles came from! It is to do with the difference in the shift side to side. Error could be caused by a confusion over "shift tiles to the left and put on right" and "shift tiles to right and put on left". I think neither was wrong, you just have to agree - see my full workings here: docs.google.com/spreadsheets/d/1iwRRXguPelDEEc493RHz-offmTKEm1qTY-p2AsENXbs/edit?usp=sharing

[@patrickwigmore3462]

Sometimes in a video call, the view you have of yourself is mirrored. That might make it easier to make this kind of error because the intuitive thing to do might be to make your mirror image match your opponent's non-mirror image.

[@Jayder845]

Hey there! I also tried to figure this out. I don't think I have the full picture, but I did leave a commment. (Might be hard to find.) Anyway, I believe you have an error in your method. I read Matt's randomly generated number as 7451811228, whereas you have substituted the 5 with a 3. The final tiles from Matt in your spreadsheet differs from the photo he took by a bit because of this. Also, there were a few other mistakes made by Vicki which you did not mention.

[@philipmiesbauer]

Oh Matt, you think too much. If you actually had a malicious opponent, then they would just not turn the tiles up-side-down.....

[@karolszostek8997]

well, if you require that the tiles are visible all the time then that wouldn't work

[@philipmiesbauer]

@@karolszostek8997 I am aware that it can be avoided very easily, I was just going off of their example game, in which that was not the case.

[@AngelWedge]

If you have an opponent with very good memory, they could just remember the layout of the grid so they know what tiles you've got.

[@user-vn7ce5ig1z]

• It's a video-chat, so you can see each other, so this wouldn't work. • Why are you playing with a cheater in the first place? The point to this is to allow two friends to play an honest game for fun.

[@philipmiesbauer]

@@user-vn7ce5ig1z It was a comment on the complex ideas Matt thought up to cheat, when it could be that simple. And it would work if you don't see the partners tiles, which was the case in their video call for example

[@TheyCallMePhinq]

okay, here's an easier solution to how to play scrabble: you're doing this over video chat Only one person has a board and tiles. let's call them the host. The host will then arrange the guest's tiles such that the guest can see them on the web cam, but the host cannot see them. the guest will then say things like "I would like to play my 2nd, 3rd, 5th, & 7th tile to make the word 'x' " and the host can pick those tiles from the guest's tile caddy and place them on the board.

[@edboswell12345]

acidfire68594 that only works with a 2 player game

[@KylerGreer]

How do you take tiles out of the bag and place them in front of the camera without looking at them to see which side of the tile has a letter on it? I guess you could feel the divet of the letter with your finger, as long as you have a set where they aren't just painted on, but then you'd know when the other player draws a blank tile.

[@asailijhijr]

But the process of playing scrabble involves rearranging the tiles in your caddy. (I know there are further trivial solutions from here, but you need to add one to your instructions.)

[@asailijhijr]

@@KylerGreer if your opponent has to write down their tiles anyway, you can flip all the tiles in the caddy whenever you add a tile.

[@tomasxfranco]

@@edboswell12345 You can add a second camera like a phone's for a 3 player one.

[@andrewdarby8843]

Not as interesting of a solution, but: One person draws from the bag for both players and doesn't look at the other person's letters. The other player has a camera set up behind their letters so that they can see them and the other person can't and they tell the other person which to play (second from the left, first from the right, etc.) This solution was posed by somebody else over my shoulder while I was watching this.

[@bradleyhite3476]

That would probably also be the way you would play with someone who has no hands, regardless of if they are in the same room or not.

[@loops8274]

I scoured the comments for this idea because it was my thought reading the video title. Looks like another case of having a mathematical hammer and seeing every problem as a mathematical nail. Also another case of ridiculous math being too much fun to pass up

[@LuckySlevin7]

The Parker Shuffle!!! It just works! Love you mate ;D Thx for all your entertaining videos

[@HienNguyenHMN]

Instead of the 2-3 shuffle, an easier way to start the game would be to randomize the starting tile. Two people use the random function again. The first significant figure of one person determines the row, and the other person's determines the column.

[@y.kennard3381]

I see the title : "Ok, there is an obvious but laborious way to do it, but how can we be smarter ?" I watch the video : "Looks like we can't be smarter."

[@quadmasterXLII]

You could do this mechanical shuffle much faster by writing each letter on one of the 96 squares of a 4x4 rubics cube -- you'd have to leave out 4 tiles but that seems fine.

[@adammercer9679]

I would say this would take forever to set up a game but right now I think we've all got a lot more free time on our hands.

[@andthen0170]

-one player randomly shuffles the tiles into a 10x10 grid and calls them out so the other player duplicates -both players turn them over -each player uses a random number generator to pick tiles one by one using x and y coordinates. They record on paper where their letters came from. -the other player puts a paper red dot on top of the opponents tiles to track which are in play -when a word is played that player tells the other to pick up tiles 8,5 4,2 etc to form the word -if the random number coordinates select a tile that is either already played or in current play then they generate another (or pick the next closest as the board thins out)

[@thefountainpendesk]

Oh my goodness, I need that scrabble set that Vicki has

[@pratikkore7947]

Matt: let's verify this. Board: N O

[@severnsevern580]

I love all the puzzles. very interesting.

[@puttanesca621]

Simpler: Player One has the master bag of scrabble pieces. All other players have their tiles placed in alphabetical order. When a player would take a piece instead Player One takes a piece from the master bag without looking and shows only the player drawing in a secret window. That player then takes the piece from their alphabetical tiles and places in their rack. The master bag should probably be a face-down shuffle to enable showing the correct side of the tile. A dedicated camera for the draw which is opened to the player drawing tiles would be handy. Player One will need a second set of scrabble pieces to place the words played by other players unless each player adheres to a strict ordering of tiles in their racks in which case Player One can set aside tiles drawn by other player in order and use them to build the words played by the other players.

[@Lance0]

14:56 lmao this is a NP-complete problem now

[@Agrajag22]

Can we call this the "Parker Shuffle"? :-)

[@MrGallagher]

Very creative, Matt! However, a much simpler solution, in my opinion, is the following. 1. One person and one person only picks the letters. For themselves they take the letters, for opponents, that person shows the tiles to the camera and simply sets them aside, out the main bag (either facedown or in another bag). 2. Create a spreadsheet which you share over the video call. This is the master board. You type everyone's answers onto this so that every one can see it. (If someone wants to recreate it on a physical board, that's up to them.) This also means that the person in charge of picking letters and typing doesn't have to fish around to find the actual tile and inadvertently see a different tile. In addition to taking very little time to set up, it also means that it is impossible to keep track of where all the sliding ends up -to be honest, I was able to keep track of at least where the very first A was without meaning to. (I made a board on a spreadsheet in about 3 minutes. To be honest, I ran the HTML file you linked to for the double board on Matt_Parker_2 channel, and copied and pasted the result into a spreadsheet, and reverted it back to the original board. But you could also simply create one from scratch pretty easily.)

[@Thewinner312]

I know how to do it: Pick random but unique numbers (for example from the tile bag) and both write them on the back of the same tiles with whiteboard marker. Then you can just shuffle any way you want. It does rely on no player purposely remembering numbers, but then again your method also relies on the fact that no one is cheating. It's more reliable and a lot faster.

[@Danicker]

I heard the problem and I thought "the only way to do this would involve both people doing the exact same shuffle on a set of tiles... but surely that would be tedious and prone to errors..."

[@SgtLion]

10:30 Matt: Gotta watch out for the tricksters, maliciously remembering tiles, or if they're really sneaky, they'll write up a computer program to track the shuffles! Me: Or they just keep their tiles face up

[@TaylorTheOtter]

What would help is making a flat surface with corners to hold in that exact 10x10 grid. Then the rows and columns (assuming they're well aligned all the same size) could shift really easily. You'd have to make the corner brackets removable so you can shift the first and last rows that way.

[@cjk32cam]

To avoid memory based attacks: A1 and B1 coordinate to produce a random arrangement by e.g. pulling letters out of the bag. A1 and B1 flip the tiles to face down, then leave the room. A2 and B2 perform the shuffling as described. A1, A2, B1, B2 can now play.

[@shalimarlake7852]

What I might have done is: Arrange them in order like you did, then shuffle in a method like the Fisher-Yates shuffle. It's a lot of busywork but it's much easier busywork than moving all the tiles since you're only swapping two tiles at a time.

[@exaltedtoast6898]

This is similar to what I came up with. I was thinking of doing a round of shunts, then generating some number of shared random pairs of squares and swapping them. I haven't tested it empirically yet (writing code now) but I suspect it will take relatively few to get it to more closely match random results, perhaps 10 swaps.

[@exaltedtoast6898]

Update to above: This didn't play out. I ran 10 million simulations on a round of shunting and then 10 swaps, these are the results (in the same order as they are listed in the description): [(-2, 5.9597636), (-1, 5.8777068), (2, 5.6325526), (3, 0.3903337), (4, 0.0307360), (5, 0.0025199)] For true random, I reference a list that is made by taking the average of Parker's numbers and my own, both 10m trials for a total of 20m: [(-2, 5.9605539), (-1, 6.5799364), (2, 4.3255465), (3, 0.2727662), (4, 0.0185389), (5, 0.0012563)] The difference of squares with this and my shunt-and-plug is 2.21536446

[@shalimarlake7852]

@@exaltedtoast6898 it's worth noting that my problem with his method was the shunts in the first place. It's a pain in the butt to do shunts compared to 100 swaps. (or however many letter squares there are)

[@IceMetalPunk]

At 17:54, you can see it on Matt's face: "Oh, no, the number of 'Parker Shuffle' comments is going to be overwhelming..."

[@DukeBG]

19:17 you can see that a lot of letters are almost in the right place just shuffled around a bit, mostly horizontally, but some are vertically. So there was likely more than one mistake made with one done either random-shifting the rows (maybe from the wrong end) or shuffling the columns. But all rows are messed up, so the mistake is more likely in the shuffle. And the other was made in random-shifting the columns, but only some of them.

[@bsharpmajorscale]

My favorite KZbin maths guy, Natt Oarker!

[@Merione]

The solution I was thinking about is to start with an ordered grid, just like you did, with the difference that all the rows and columns are labeled with numbers from 1 to 10 (or letters from A to J, doesn't really matter). Then, starting from the tile in position (1,1), generate two random numbers from 1 to 10 for the row and column respectively and swap the first tile with the tile in the corresponding position in the grid. Then do the same with the second tile (1,2), the third tile (1,3), the fourth tile (1,4) and so on, all the way up to the 100-th tile (10,10). After all 100 tiles have been swapped, both players have the same arrangement, but it's easier to calculate, there's less chance to make a mistake and it's probably faster too. I don't really know about the "randomness" of it, though. Any help?

[@kindlin]

That would clearly be 100% random, assuming a good RNG for the swapping bit. It would take a lot of effort, tho, and would be prone to errors with that many repetitive swapping operations. The method presented gives a systematic method for arranging them that is, in principle, a little easier to 'get right', as each step is larger, moving more tiles.

[@robinisomaa]

Wouldn't that make it easy to keep track of a particular tile? Just memorize its starting position and keep track when it is swapped. However, it might be more difficult to keep track of multiple tiles and if tiles are always drawn from the top, you know when it is drawn, but you can't draw it at will. Overall, I like this system. It might be faster than shunting and shuffling, and if you have the rows and column clearly marked, I don't think the chance of screwing up is fairly low.

[@opijfdgrty]

It's interesting that despite an error being made somewhere, both shuffles managed to generate the word Poo.

[@SuperSt0ne]

opijfdgrty This is a well-known error with Python’s randomizer.

[@christianbarnay2499]

Aside from the synchronised shuffle issues you also need a procedure to return letters in the "bag" when a player decides to exchange tiles. You can't just put them at the end because that would break the randomness.

[@jasonsmall5602]

A much simple solution: Just arrange it in a 10x10 grid and then roll a 10-sided die twice for each round, selecting a row and column number. If you pick something already picked, roll again. Also feel free to consolidate to a smaller grid as necessary. Maybe use the die roll mod the number of current rows/columns to make sure you always hit an existing square.

[@mint301]

The puzzle, I heard it and was like "This is going to take me forever!". Then I started working on it "Well, very specific letters much be used in all hands to reach 46". Turns it into "What X tiles do you need to reach Y points", where both X and Y are pretty low numbers. Much easier! :P

[@SpencerTwiddy]

Did your answer kind of resemble a year?

[@1Resare]

Mine had three digits

[@OlliFritz]

@@SpencerTwiddy well technically yes if the Roman Era counts

[@1dgram]

It doesn't even have to be which X lettered tiles, but which when choosing 7 tiles out of a possible 0, 1, 2, 3, 4, 5, 8, 10 point values equals the total. From each of those find the number of valid combinations. Compute the total sum of valid combinations for the final answer

[@LiquidZulu]

Why does using a scrabble app preclude conference calls? Use both at the same time.

[@sayanghosh6996]

That's my point too. They're creating a solution to a problem that doesn't exist

[@SiEffen]

that would strike me as the best option and saves having several hours 'shuffling' the pack whilst worrying that it's not been done right!

[@Tefans97]

I do that with a friend of mine, works great, but an easy boring solution isn't what we come to Matt for

[@pieboy2043]

A possible solution is to assign each column a letter and each row a number, or vice versa, and keep a “ledger” of sorts using it like a coordinate grid to keep track of who’s picked what, so that you can more easily put other players’ words on your board

[@Killerspieler]

You can add another seed to start off: randomize the letters for one persons set (you already did, when you emptied the sack) and the others copy that order to their respective 10x10 square. With Matts method you have to sort them anyway and then turn them around, so that won't be much slower. A 90 degree angle (maybe made from scrap wood or so) will probably help doing the shuffling (pushing around and aligning single rows/cols easier). Nice idea, Matt, and now we have the statistical proof, that it is random. cool!

[@FlatEarthMath]

The two main flaws of Matt's very ingenious shuffle are: 1) It's really hard to manually shuffle the tiles and not make a mistake in the algorithm, as shown with Vicki. 2) Playing the tiles requires both participants to have a detailed inventory of unseen tiles ("I'm playing my 3rd, 6th, and 7th letters"), especially as tiles may "live" in your hand for many turns before being played. A main (and fun) aspect of the gameplay is manually moving one's tiles around in your hand to anagram your way to a new word, and having to keep track of which item number each tile was in the inventory would be very hard (or at least requiring a paper list). Without using a third person as moderator, any "play scrabble over Skype" kind of game will require the honor system on the part of the two players, with regards to the shuffled tiles. Acknowledging this, I propose the "shuffle" be done in a shared Google Sheets spreadsheet, with the font color be white-on-white. Column A: list all scrabble tiles in order from _A_ to _"blank"_ for 100 rows. Column B: _=Random()._ Then turn column A's font to white, and sort on Column B. Both players copy Column A to a new, non-shared spreadsheet, which will be used to "draw one's tiles" by changing one or more cells to a black font. During gameplay, the communication will go like this: "I'm drawing three tiles: from A16 to A19" at which the other player deletes the contents of those rows (not the rows themselves) without peeking. As for the physical board and tiles, both players start the game with all 100 wooden tiles face up and in alphabetical order like at 2:28 in the video, so that gameplay using the actual tiles is very easy, as is manipulating one's own "hand." Again, this will require the honor system not to peek at your opponent's cells, but if both players are good sports, this shouldn't be a problem.

[@VincentGroenewold]

Absolutely great stuff but I would just stop after the first shuffle method. Good enough. :)

[@notmario741]

Going to try this out!

[@daviddelille1443]

1) set up tiles in an ordered 10x10 grid (rows/columns marked 0-9) 2) flip all tiles in place so they're face down 3) generate 2 random digits using a calculator: x and y 4) move tile at row X and column y from the old grid to a new 10x10 grid at the first open position 5) repeat steps 3 and 4, discarding any invalid row/column numbers (e.g. no tiles left in a specific row) For extra randomness, you could also randomise the location in the new grid, instead of placing them in order. This does double the number of coordinates needed and increases the likelihood of mistakes. This method could go relatively fast, if you alternate players who just call out coordinates. 5 seconds per tile, 100 tiles => ~10 minutes to set up the game.

[@CK-ceekay]

To be honest, just shuffling and shunting the tiles seems like an equally fun game

[@AndreasEldhSweden]

Next weeks maths problem: Recreate how Matt and Vicky shuffled respectivly, to find out where they did it differently.

[@danilafoxpro2603]

There is also Fisher-Yates shuffle, which results in completely random sequence with any starting sequence. You need random numbers for it also.

[@atrus3823]

Alternative: 1) one player puts all tiles in a bag and shakes it up, 2) draws all 100, one at a time, reads out the letter, and places it face down, forming a 10x10 grid as they go, 3) the other player follows along, forming the same grid (both players agree to not memorize locations). When a player needs to draw a tile, each player rolls a 10 sided die: one for the x coordinate and one for the y coordinate. One player takes the tile, the other discards the same tile without looking at it. If you hit an empty location, just roll again.

[@TaohRihze]

Matt Larker, I mean Natt Oarker

[@BL3446]

I do wonder how you plan to deal with the tile exchange rule. How do you put back your own tiles into the grid randomly, but fairly?

[@onecommunistboi]

More importantly they have to placed so you dont know where they are. The only thing I can think of is to just place them anywhere in the grid and then shunt and shuffle the whole grid again.

[@relfeaj91]

Put them in the front and shuffle again! 15 min later you can continue!

[@TheZotmeister]

THIS. This was the comment I was looking for. This was the question in my head THE WHOLE VIDEO.

[@davidrbarnes81]

Or perhaps you omit that rule in quarantine Scrabble?

[@walkerwillingham8599]

Yes, also my question from the beginning. The same problem defeats other "solutions" to this problem, but there may be a way to do it with my favorite solution, which is have one person do the drawing, and show each of the opponents draws only to the opponent. Doing it this way, the tiles shown to the opponent need to be arranged in the same order upside down by the drawer, well the explanation gets squirrely here, but it involves identifying particular letters both for applying them to the board for plays, or for identifying tiles to return to the bag in a trade. That part of the process strikes me nonetheless as too prone to error, as the shunting and shuffling is in the process Matt presented. Removing the option of trading tiles in lieu of a turn, is absolutely unacceptable.

[@cold_fruit]

you could put shiny plastic labels on the back of each tile, and use a dry-erase whiteboard marker to number all the tiles in order to keep track of which tile is which post-shuffling

[@jomiar309]

He is so proud of how he randomized his shuffling simulations :D I think this is so much more difficult than just having a scratch pad program on a website where each person enters their tiles each time, and it will tell them if their partner's draws require them to discard. Basically, it counts the tiles, but each player doesn't see what the other draws, and the program will tell each person individually when they need to discard the tile they just drew and draw again. It's not fully blind, but it's way less setup (and error prone) than this shuffle method.

[@spindoctor6385]

Your method would leave the problem of still sometimes knowing what tiles your opponent has. If you were to pick up the Q and the program tells you to discard it, then you would know your opponent has it, you would then be very cautious of If/when/where you play a U if you had one. Oh I just read your post again and you acknowledge that it isn't totally blind, but i have already typed this so i am going to hit the reply button anyway

[@bbgun061]

My wife and I were just thinking about playing Settlers of Catan over a call with my brother...

[@SillyPutty125]

I've actually done this before! It's much easier than scrabble because the only hidden information is the progress cards, which you can do by revealing the top card of the deck to the camera (without looking at it) when your brother buys one.

[@bbgun061]

@@SillyPutty125 That's what I'm thinking. It shouldn't be hard, just have to carefully set up...

[@zerid0]

Now calculate the odds of the resulting square being a magic square (same number of points in each row/column/diagonal)

[@Hevlikn]

What i suggest is a random draw for the 10x10 board; each draw verify face and position and then place face down. Then use the shunt method alternating up/down. If each player has 2 scrabble sets; you could additionally completely ignore whether or not you have the same random set, playing the opponents pieces out of the spare, and discarding the face down tile from your random set. This might end up with non-standard scrabble games, but would massively reduce stress from synchronising games

[@Showsni]

My niece likes playing Junior Scrabble with me, so I thought I'd work out a version to play that. Junior Scrabble has two games in it, Words and Pictures and Rainbow Scrabble; this is for the Words and Pictures side of the board (as that's the one my niece likes to play). One person shuffles up all the tiles in the bag, draws out seven for themself, then seven for the other player, and tells the other player what they are, keeping both sets of seven face up in front of them. (One important rule to note about Words and Pictures Junior Scrabble is that all tiles on racks are kept face up, and able to be viewed by all players at any time... That does make this puzzle somewhat trivial, though!)

[@thomasdegroat6039]

There are no ways because if you’re able to use all seven tiles you automatically get a bonus 50 points

But the bonus is just for using them. The puzzle says that you just choose seven letters that total 46 points, it says nothing about using them on the board.

[@rebmcr]

Geoff looks different in this one.

[@andthen0170]

I first thought if this is this weeks MPMP, then this will be a long winded and complicated assessment for Matt to come up with the leaderboard :)

[@joshj3949]

We were thinking of a variant where player 1 (and only player 1) takes seven, plays what they can and puts the rest back in the bag. Player 2 updates their board with those and then takes a new seven, plays what they can and puts the rest back in. Rinse and repeat. Definitely not the same game anymore, but potentially similar enough, and saves a lot of time coming up with an identical shuffle or having a fancy multi camera setup.

[@Flocko_]

When you were shunting horizontally did you coordinate whether to take from the left or the right?

[@samba272]

17:31 That is how my third dates usually end

[@PrincessPolyhedra]

Fun fact, the tiles from 2 sets CAN fit on a single board. A scrabble board has 225 spaces (I love square numbers) and a scrabble set has only 100 tiles. So, while difficult, it should be possible to place two sets worth (200 tiles) on a single board. Scrabble is my favorite game and I love math above all other subjects, so this video is the best thing I could have asked for before bed. Thanks for the upload Matt!

[@PrincessPolyhedra]

Also, I once built a spreadsheet that you could play scrabble with. Using a spreadsheet, or some other way to randomize tiles, you could have a randomizer pick the tiles for the players, tracking what has been grabbed. This would allow both players to leave all their tiles face up and always grab what the randomizer told them to grab.

[@WilliamMay]

Matt, I have a simple solution: split the tiles at the start. Set up the grid, then take turns picking tiles off the board via random number. Each person then has two identical tile sets, one for themself and one for their opponent. The tiles for their own set can be randomly pulled from the bag as normal without worry of messing up the tile set with duplicates.

[@Deedumdee]

I thought something similarish. Split the tiles in half equally by letter, so you've got two sets with the same number of A, B, C, etc, for ones with odd quantities round up by making paper extra tiles for what will be your opponent's set. Then chuck your set in the bag and play as normal. It does limit the pool you're picking from and the extra letters will warp things a little, but it should roughly work. Or play with an app and videoconference at the same time.

[@matteovidali3829]

Could you randomly number the backs of the tiles, and just generate a random sequence and arrange them accordingly?

[@MateusSFigueiredo]

but after some plays you would memorize that tile 833 is a letter A.

[@JNCressey]

7:10 Imagine if you were just trying to play scrabble and discovered an exploit in python's RNG

[@darealpoopster]

Imagine if you were just trying to play scrabble and discovered an exploit in the Universe’s RNG

[@esquilax5563]

Haha! Well in most programming libraries, the bog standard random number generator is usually stated to be not cryptographically secure, so probably already has some known exploits

[@KlausKlass]

At the beginning of each game, generate a randomized order of the numbers 1-100. Both players put the tiles in order and flip them over. Write the numbers on the back of the tiles in the randomized order using a pencil or erasable pen/marker. It is very difficult to memorize a random list of 100 numbers, so everyone will forget the order. Use these tile numbers when referring to a tile during the game.

[@MathMusic437]

Hey Matt. Check out the Scrabble variant Super Scrabble. Uses a 21 x 21 board and 200 tiles. The set is not usually played with a double distribution of standard tiles, but it's close enough that you certainly could play a decent game with two normal scrabble sets combined.

[@kernerator]

Is anyone going to analyse the shuffled arrangements at the end to determine whether Matt or Vicki made the mistake?

[@shelvacu]

i had the same thought!

[@plexluthor]

Matt doesn't read his number out loud, though. He writes it down, but it's hard to read. Maybe 7656811278?

[@plexluthor]

Watching again in slomo, I can't see what he does for his first row, but I'm pretty sure the rest are 451811228. If I use 7 for the first row I get ML in the top left, but I also get NO right next to it, which he checks and doesn't find. Most of the other stuff he checks matches mine perfectly. Everything at the bottom matches for sure. ¯\_(ツ)_/¯

[@funwithyoyo]

@@plexluthor wouldn't it be easier at this point to decrypt matt's shuffle technique using a program and the tiles he reveals?

[@alecsjoholm3970]

There's a website, isc dot ro. It's free to play, and many experts use it.

[@kjyost]

I appreciate that your tiles are written in the famed Parker Font.

[@jurregroen8898]

Here is an interesting fact: If the square has an odd number of tiles on it's sides, then the shunts and shuffles combine to make a permutation of sign 1, so if you know where every tile but 2 of them went, you can deduce which way around they are. (this is because shunts and shuffles will be cycles of odd lengths, which are even permutations). Aside from this, there is actually nothing else preserved in the shunts and shuffles. You can prove this using a commutator algorithm of shunts and shuffles that does nothing but make two swaps of two pairs of two tiles, in a similar way that you might solve a rubik's cube (in fact, this is basically isomorphic to a rubik's cube with the shape of a torus, if you can imagine). In the case where the side lengths are even, every single permutation can be made, so it is possible to make it truly random.

[@Exeedo.]

Has the solution to this puzzle been published yet?

[@amystrauss9597]

That's what I came to ask!

[@amystrauss9597]

Came back to share an answer I found on MP's Twitter page: "The leaderboard was updated etc but we’re holding off on the video until we have time to play enough games."

[@Exeedo.]

@@amystrauss9597 Okay, thank you.

[@VollderFred]

You know you could just use the scabble app while also having a conference call at the same time?

[@stephenkamenar]

you know this is a math channel? not a practical channel

[@deathsheir2035]

There's also Tabletop simulator, in which you can play many tabletop games, like Scrabble, Life, Yahtzee, Monopoly, Cards Against Humanity, etc...

[@darren.mcauliffe]

Instead of drawing left to right, top to bottom. You could roll two d10s of different colours. One for row, one for column. If you roll a tile that’s missing, then you go left to right, top to bottom, from there. That way the shuffle doesn’t need to be as good.

[@NashvilleMonkey1000]

Just have a board in addition to the tiles to strike off selected tiles from the board, and select the tiles randomly from a bag, and redo any tiles that are determined unavailable. Or just have one player do all the random draws for both sides, so all the tiles are on the host's side.

[@mytube001]

How unfortunate that Matt arranged the tiles in a square pattern... :D

[@MrBroady02]

30 seconds in, and I'm going to guess the answer is kind of yes, you sort of can. Parker Scrabble if you will.

[@MrBroady02]

Well, he did not disappoint ! Nice work Matt, I love the parallels your method has with cryptography in producing well ordered chaos.

[@StateExam]

Amazing video

[@davidwassink9501]

Matt, you know that you will have our undying admiration for your enthusiasm and willingness to try anything... With that being said... Nice #parkershuffle

[@SpektralJo]

Easy, just get Tabletop simulator

[@mathOgenius]

Really need this in these days.. #quarantine

[@MichaelHeide]

If we're taking about just two players, there's a much easier way. Only you use your bag of tiles. You set up your tile holder, you set up your opponent's tile holder and point your camera at that, so that your opponent can see their tiles and the board behind it. You set up the video chat so that you can only see your opponent, not your own camera feed. Number the positions their tiles are in. Their left most tile is tile #1, the one next to it is #2, and so on. And then have your opponent pick the letters by saying tiles #3, 5 and 7. Form the word [blank] there and there on the board. You place the tiles for them, take a note of their points, replace the tile on their tile holder and make your move.

[@PhilBagels]

The correctness of the shuffle can be verified on every turn. Put markers on every tile that a player takes in their "hand", and when a player says, "I'm playing the 1st, 2nd, 4th, 5th, and 7th tiles to put the word "MATHS" on the board," then you can turn over the tiles under those markers (numbered 1-7) and verify that they are indeed those letters.

[@jonadabtheunsightly]

Another option is to keep the same board, but split the collection of tiles in half before the game starts. The wrinkle here is that there are odd numbers of tiles for some letters, but there are various ways of dealing with this. For example, you could precede each game with a series of challenges or coin flips or whatever for the right to choose between having a fifth A or a or a fifth I; between having a second G or the one K; between the J and the Q; and so on. Once the tiles are divided among the players, each player turns all "their" tiles face-down and shuffles them. This, in common with the larger-board solution, assumes each player will need the same number of tiles, which is not absolutely correct, but for a casual game between players of similar ability it might be close enough. It also prevents one player from randomly getting all the vowels, but that's if anything an improvement.

[@ruroruro]

In case anyone is wondering. They made an error somewhere during the horizontal shunting. The final board configurations are shown at the end. You can see, that the letters in each row are the same between the 2 boards, just not in the right order, so the vertical shunts and shuffles must have been the same. Next, within each row the "wrongness" is different. So for example, in the last row the L "moved" from the 1st position on Matt's board to the 3rd on Vicki's. But in the row above that, The letter P from the 1st position did *not* move to the 3rd. This means, that whatever permutation, that they did wrong, it affected different rows differently. So it was the horizontal shunting. Perhaps, they shifted the rows in different directions or started shifting from the top/bottom.

[@pierreabbat6157]

I suggest, after rotating rows by random digits, doing a fixed shuffle of diagonals before rotating the columns. Then after rotating the columns, do a fixed shuffle of the diagonals the other way. With no permutations in between, if Matt does any rotation of rows, then Vicki gets any number of all 10 of the same digit and rotates the columns, then Matt does any rotation of rows, it's equivalent to just some rotation of rows.

[@davidconnell1959]

It’s Vicki! Hooray. After months of owning my first smart phone and grumbling about the calculator’s limitations, one sentence from Matt Parker has been life-changing: turn the phone sideways to get the scientific calculator!