MPMSolutions: Can you play Scrabble over a video call?

This is the solution for the Scrabble Puzzle!
www.think-math...
• MPMP: Can you play Scr...
Thanks again to Vicki for joining in.
www.vickipipe....
This is where I got the 'scrabble letter distribution' diagram from.
en.wikipedia.o...
Points that sum to 46:
10,10,8,8,4,3,3
10,10,8,8,5,3,2
10,10,8,8,4,4,2
10,10,8,8,5,4,1
Here is Amy Strauss's hand-written solution:
docs.google.co...
Joe Bott's C# code which is definitely not Python.
gist.github.co...
‘The words that best represent my experience solving the puzzle are HMM, OK, UH, VEX, AH, KEY, FIX, JOY.’ - Jordan Tullis
Kiera Romeo's comprehensive paper about the solution.
www.dropbox.co...
Bryce Chanes plot.
docs.google.co...
Duncan Harvey plot.
github.com/dun...
Noah Morris's 'code in a tweet'.
/ 1250267233546313728
www.wolframclo...
DOUBLE BOARD (by Rachel)
www.dropbox.co...

[@Not.Your.Business]

Parker Python - the programming language for the sharp minds

[@ten.seconds]

Well it's above C level just like python

[@Mr123ichkomme]

I'm fore Sure happy i don't have a Parker Processor those small errors of 1 would rly add up ;)

[@puttanesca621]

One player has the "Master bag" of tiles, both players have another set of tiles to play with. The player with "Master Bag" draws all tiles, showing their opponent the tiles the opponent would draw without looking at them herself and sets them aside in order face down.

[@ten.seconds]

What Noah Morris did (program that fit in one tweet) is called "code golf" in which you try to minimize the number of characters used but still solve the problem. Some specialized programming languages are invented just so people can be more expressive (well, not for human readers, but for translating into computer instructions) with as few characters as possible.

[@karlwaugh30]

To address Vicky's problem with Matt's original solution to the open problem. If the two players took pieces from alternative ends of the ordered shuffled tiles, then there wouldn't be the "I've taken 5 get rid of them" problem and you would just have to finish taking pieces at the right time (aka keep track of how many you've each taken and periodically check if it's nearing 100 collectively)

[@mattparker2]

That is an excellent suggestion!

[@sinisternightcore3489]

What if you have 3 players?

[@rmsgrey]

​@@sinisternightcore3489 For more players, you can assign each player a chunk of the grid (for 3 players, you can use a 9x11 grid and give each player 3 rows, with one tile left over) - when someone exhausts their chunk of the grid, you can pause play to update everyone's grids with what's been taken - and then you've probably got few enough tiles left that you can just update each turn (if there's still a significant number left for whatever reason, you can redivide the remaining tiles and continue until someone runs out again)

[@rosiefay7283]

18:20 Indeed, if exchanging is still legal, you can exchange as many or as few as you want. Even just one, which is quite often useful. 19:36 A pity neither Rachel nor Tobias Devereux knew about Super Scrabble, whose board is the same 21x21 that Rachel used, but with a different arrangement of premium squares. 20:54 What I find came up more often in Scrabble is "Oh good, my opponent got the Q (or the J) -- I won't ever get it now".

[@jellomochas]

I gave up on this problem quickly, not having realized that I had to choose exactly seven tiles; the amount of combinations of (arbitrarily many) tiles summing to 46 is extremely great.

[@scragar]

I have amusia(the part of my brain responsible for turning sounds into music is broken so music is just noises to me), the idea of a third channel just for music free versions would be awesome, although I'm not convinced it's worth the effort given I'm already enjoying your videos and I've never had a problem with your videos anyway(although I'll be honest I still turned subtitles on and audio off for the original version of the band problem, it was really annoying but then you already fixed it by uploading a new version).

[@Falanwe]

Parker Python is my favorite programming language. I used it for solving this puzzle, and my formatting was far better than the one shown there (it still gives me shivers 25 minutes later). Also, in Scrabble, the 50 bonus points for playing all your tiles at the same time can never be multiplied.

[@andrewmirror4611]

I expected you to play Scrabble online live

[@ErkkiMattila]

QI published a Scrabble video on same minute as this started. Matt propably has infiltrator in the elves.

[@rosiefay7283]

And I watched it. Probably why KZbin then recommended this video.

[@bruzie900]

Matt has appeared on QI himself.

[@kane2742]

I noticed that they were published around the same time (since they showed up next to each other on my subscription page), but didn't notice that it was EXACTLY the same time!

[@veggiet2009]

​I'm surprised in that Combinatorics question no one brought up when you play letters on double letter or triple letter spaces

[@veggiet2009]

So you could have 10, 5x2, 8, 8, 5, 4, 1 or [5, 5, 4, 4, 2, 2, 1] x 2 and more, but then you have to work with the logistics of the board to determine which combinations you could do, and what is the fewest number of tiles that you could play to make 46?

[@veggiet2009]

And I'd want to consult the scrabble dictionary to see how many of these combinations are actually legal

[@JohnR31415]

My now wife and I sat down for a game of scrabble with another friend. She played one word (beavers) on the starting square... then the neighbours knocked on the door because their main fuse box was smoking and they needed to call the fire brigade.... we never did get any further.

[@GuanoLad]

You've done Monopoly, you've done Scrabble, I wonder if you can somehow do Cluedo.

[@colonelbarker]

I'm curious- what vision mixer do you use?

[@rosiefay7283]

22:15 Good idea. The players agree to use the same app, and seed it with the same seed (so that the app does the same shuffle for both players)... But Matt, why did you specify "no software solutions"? In this era of software, particularly web apps, this is the obvious way to solve the problem.

[@Garbaz]

I think that was requested by Vicky if I remember correctly. They wanted to play with physical tiles, so no online scrabble, and that was expanded into no software at all.

[@andykillsu]

Still waiting for the Channel name to change to Matt Parker^2 :P

[@rewrose2838]

Matt Parker ² (Press and hold the '2' key if on mobile, or use alt+0178 on keyboard)

[@veggiet2009]

I choose to see it as Mattₚₐᵣₖₑᵣ_₂

[@Qermaq]

Aw simple. Host player has as many cameras as there are players plus one. Do a Zoom meeting, and each player and the host's cameras all join. Host has a camera on self, another on the board from above, and racks facing away from him toward a camera. Host plays tiles and replaces for each player.

[@TheGrandUser]

"They got the points for the best low-tech solution. No points, hypothetical points, I got to be careful. I'll say that people get upset." I believe the proper term you're looking for is "Kudos" :)

[@kane2742]

Or "Parker Points"?

[@aliiannucci3135]

I am the Ali of the Ali and Vinnie lowtech solution and I am thrilled to receive zero bonus points

[@iabervon]

I'm curious as to whether a Scrabble variant where all players racks are visible to everyone would be fun. Also whether it would then be more fun to draw at the end of your turn (giving others a chance to see your new tiles) or at the beginning of your turn.

[@VincentZalzal]

Yes, after 4 months, closure! Now I know why I didn't get the correct answer for the submittable part. I thought I had to list all 7-letter words that had a value of 46, i.e. I mistakenly thought order did matter (and identical letters are indistinguishable), but as stated (later?) on the web page, order did not matter.

[@samus88]

Wait, but how do you put on the board the words the other person's using? wouldn't that give you access to their letters and thus make the whole scrambling blindly the letters pointless? Because you can't play scrabble independently. You need to make each word share a letter with a previous word.

[@QRebound]

10:28 That's some strange looking python...

[@QRebound]

lol *phew* he catches it at 11:15

[@ZorMonkey]

Oh man. The rest of the "Parker Python" solution: gist.github.com/jjbott/765e105b1fa17a8ee01432bf33c48ce9 . Sorry about the formatting. :)

[@QRebound]

14:00 the notification is in the video, you can all stop checking your tabs

[@KartheekTammana123]

I replayed that part 3 times just to be sure

[@samus88]

There's only 1 K in the english Scrabble?!

[@genericusername4206]

you could just use scrabble notation havent watched the video yet maybe they did that

[@minirop]

No apologies to Vicky for accusing her for screwing up when it was you? (See my mail with code) As scrabble gameplay, there is the variant where one player draws 7 tiles then eveybody has the same rack and the player with the highest scoring word can put it on the board and gets the points, then all remaining players discard their tiles then another player draw 7 new tiles.

[@BryanLeeWilliams]

More cowbell!

[@SwordQuake2]

13:27 what language is that? And can someone explain its semantics?

[@torsten_dev]

It is mathematica see links in description. The one with a link to twitter and wolfram

[@thecommexokid]

Author here. Yes, it is the Wolfram language, which is used in the Mathematica software product. First I define 3 lists (“L” for the names of the letters, “P” for their point values, and “C” for their counts). Then I treat the 27 letter-names as variables representing how many of that letter are included in the hand, and set up a system of 2 equations and 27 inequalities that I solve (“Reduce[…]”) for all integer-valued (“, Integers”) solutions. Lastly I count the number of such solutions (“Length@…”) which is what gets output. As for the equations themselves, “Total@L==7” means the total number of tiles I include in my hand should be 7. “L.P==46” means I should include 46 total points, a.k.a. ℓ1•p1 + ℓ2•p2 + … = 46. And the 27 inequalities are each of the form 0 ≤ ℓ ≤ c; that is, I can only select between 0 copies and all copies of any particular letter. The coolest part of the code for me is the use of “Through[…]”, which turns a single equation involving lists into a list of individual equations involving the lists’ corresponding elements.

[@thecommexokid]

You can search the Wolfram language documentation center (reference.wolfram.com/language/) for full info on any of the functions used: List (“{…}”), Length, Reduce, Total, Dot (“.”), Join, Thread, Integers. Other syntax it helps to know: f@x is the same as f[x] and x~f~y is the same as f[x, y]. (Both are 1 character shorter, which is useful in fitting code into a tweet!)

[@SwordQuake2]

@@thecommexokid Thanks for the awesome explanation.

[@zoklev]

for myself 21:23

[@derwolf7810]

First: It was a relieve to see that i didn't cause the delay with my solution (for which exchanging one or more tiles for an equal number from the bag, would have been a little bit time consuming...). But i would have liked watching this video live - did i miss the announcement? Second: I technically disagree with the solution of 138; although i might misunderstood the word "tiles" (or "ways"?) instead. For me a tile is the physical piece with the label and points-value painted onto it. I think my objection is best describe with an example: If you draw one tile out of a collection of three G tiles, then in my view you can do it in more than one way, because the tiles are physically different; so you have G_1, G_2 and G_3 all with label "G" and points-value "2" painted on it, which results in three ways to get a tile with label G (G_1, G_2 and G_3). But the solution seems to be based on the view that there is only one way to draw: Label "G". I would have expected the distibution of points to number of tiles is (see tavle at 8:22 in the video): points: 0, 1, 2, 3, 4, 5, 8, 10 #tiles : 2, 68, 7, 8, 10, 1, 2, 2 So the amount of different ways for the single additions should be (in the same order as is given at 8:40 in the video): 280 = "10 choose 1" * "8 choose 2" 56 = "8 choose 1" * "7 choose 1" 315 = "10 choose 2" * "7 choose 1" 680 = "10 choose 1" * "68 choose 1" (For better overview i left out "n choose n" for n=10, 8 and 5 points and "n choose 0" which are all 1.) Therefore i would expect 1331 as the solution for the above question. Side question or optional "Third": Just in case the above is caused by broken english on my end, then how would you have asked, for the solution i presented here? PS: I don't want to have more points, i just want to better understand.

[@bsharpmajorscale]

Cinema.

[@johngranahan6102]

Dear Matt, I like your stuff, I like maths, I did not like the delay this took, Truthfully I didn't attempt a single other puzzle video because it didn't seem right leaving one puzzle unfinished and moving on from it, I am writing this in hopes you'll read it and maybe take a lil criticism on it, the first video didn't have to be published when it was, you could have waited until you had most of today's footage captured and then done them like the rest of the videos or atleast put out comments giving us all a time frame, I understand you're busy but it's annoying to be left in the dark with one line on a website saying it'll take a while, next time maybe just wait until you have it almost done before giving us months long waits, Yours sincerely, John

[@MrDannyDetail]

I find it odd because it was implied that the delay was because they needed to try out the various ideas sent in for the open problem, which entailed them playing lots of scrabble games to test them, but then it seems from this video that Vicki probably only ever tried Matt's own suggested solution, which she already knew before the first video went public, and which, as you say, could have been pre-tested before they launched the puzzle. So the only other thing I can think is there must be some behind the scenes reason why they couldn't do this video sooner, which makes me think it was to do wih Vicki's availability (since we know Matt has been available throughout). So my guess is that Vicki had some sort of personal reasons for not being able to do this video sooner (such as illness, bereavement, or needing to spend all her time doing something else (maybe caring for someone?)). Whatever the true reason I'm sure it was unanticipated and Matt didn't originally intend to have such a delay between puzzle and solution.

[@johngranahan6102]

@@MrDannyDetail I understand where you come from on this but at the same time, it's not hard to schedule something in advance of uploading a video and if it was a thing of Vicky may or may not be available then I don't think it would have been too much to address in either a full comment on KZbin to subscribers or atleast give us some semblance that yes we are still going to do a solution, because as an audience we were really left in the dark and no harm really done but it's disappointing nonetheless and so I voiced my critiques, I do appreciate your reply though and I hope I haven't come across too harsh here

[@holeysh]

why is it so laggy? its unwatchable :/

[@recklessroges]

Ironically the answer is in the video. (To be fair, most of it is a perfectly good podcast, so you can just listen.)

[@bmdragon]

"and that's all the math people sent in" *me who sent in java code for this problem and didn't get featured* :(

[@milco2006]

Ye I sent in a very detailed approach which was much better than Matt's but didn't get featured

[@rmsgrey]

Minor nitpick: the video implied that the 50 point bonus for playing all your tiles can be multiplied by scoring a double or triple word bonus on that turn. That's not true - the 50 points are added to whatever you would score on the turn, not attached to any specific word. In theory, it's possible to score in the thousands (depending on wordlists, and assuming a co-operative opponent and perfect draws, single turn scores of 1778, 1780 and 2044 got listed around a decade ago). Whole game scores for theoretically perfect 2-player games have been reported as a bit over 4000 with highest score for one of the players coming in just under 4000 (using the more restrictive American word list - though I believe the word lists have been updated since). The basic pattern for such a game sees one player taking all the turns until the bag is empty, then the other player playing out 6 of their 7 tiles, then the first player playing their remaining tiles, scoring off the second-player's tiles. Strictly speaking, playing out such a game also typically requires a lot of time spent replacing some or all of your tiles in order to assemble the necessary rack for your next play - for the purposes of demonstrating such a game, picking the tiles face-up rather than drawing randomly will save time without altering the outcome.