The Only Clue Is The Number 1000... How?!

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** TODAY'S PUZZLE **
Aliens have been helping to set sudoku puzzles, the only problem is that Christoph Seeliger has forgotten what they told him about the number bases they used! Just look at this puzzle - in which the only clue is 1000 - and marvel!
Play the puzzle at the link below:
app.crackingth...
Rules:
Normal sudoku rules apply. Clues outside the grid are X-Sum clues. Ie They give the sum of the first X digits where X is the first digit from that direction. Some friendly Aliens helped me creating this puzzle, but each alien uses his own number system with an unknown base, and I can't remember which alien wrote which clue anymore.
** NEW PATREON SOLVE **
Simon has recorded his solve of Mr Menace's EXCEPTIONAL puzzle Masyudoku. This is so good that Simon is a tiny bit concerned that it might be enjoyed by a wider audience, despite its ruleset (which is much easier to get to grips with if the solver has a working knowledge of the Japanese logic puzzle Masyu).
You can find the puzzle here and watch Simon's solve on Patreon:
logic-masters....
And there's also The 12 Labours Of Hercules - a fantastic sudoku hunt by Peter Veenis, Aspartagcus and Panthera - with original art by Peter! A shout-out on the channel for successful solvers of the whole pack :)
/ crackingthecryptic
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It's already out on Android and App Store. 60 original puzzles by Sam Cappleman-Lynes, Clover and Philip Newman!! Earn party hats and dinosaurs with these brand new puzzles!
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[@UghUgh1234]

The puzzle content I want to watch is the type of puzzles I could never do. It’s like watching Olympic swimmers. I watch it because I could never swim that fast and it’s fascinating.

[@manuelmanzur-luengo1067]

Same here!

[@zaranmehta13]

Indeed

[@Anne_Mahoney]

Yes, definitely.

[@Kaeri11000]

Hearing Simon go "Oh... it's Sudoku!" Is very funny both in, and out of context. Got to love that with all these rules, he always misses the obvious stuff!!!

[@cathybryant5119]

35:50 I have found a nice way in Sven's lovely software to keep track of which outer clues(x-sums, sandwich, skyscraper, etc) I have used. I use the line tool to make an X on the outside edge of the cell beside the clue I have completed. It helps ensure I use every clue without cluttering the inside of the grid with extra colours or pencil marks.

[@RichSmith77]

I made use of this technique for the first time on this puzzle. Worked well. Will use again. 👍

[@alanclarke4646]

This. Also turning on " check pencil marks" in the settings is a big help with all variant sudoku, as pencil marks which conflict with a placed digit will change colour.

[@RichSmith77]

@@alanclarke4646 Everyone can make their own choice on this, but for me it's straying too far down artificial help in solving the puzzle. It should be up to me to spot the restrictions, not the computer.

[@crystalgehrt8861]

That's what I do, too. It's so much easier to see everything.

[@nileprimewastaken]

I first saw Chaotic Wrogn (Cracking the Cryptic: The Second Movie) and thought that puzzle was so interesting that I hung around specifically for more wrogn puzzles, but now I have learned to love all sudoku.

[@tremkl]

I’m at least one of the views who watched all of “Is this Sudoku Impossible?”, and twice I’ve actually gone back and solved it myself. (I wait about 6 months in hopes of forgetting as much of the logic as possible.) Wonderful puzzle

[@MedusaMrigesh]

"Is this Sudoku impossible?" is what the youtube gods decided I should watch after some video about a mathematical problem involving pennies... 15 months later I'm still watching :) (and can actually solve most of the puzzles presented)

[@GregJonson]

To be fair, the fact that Simon and/or Mark are able to solve these puzzles doesn't mean they're not impossible.

[@christophstahl8169]

I really loved this one. The aliens and bases was a nice touch and the 8 and 27 totals being of different lengths was beautiful. Very nice flow, not too difficult, just looking at possible totals. I enjoyed that alot.

[@emilywilliams3237]

These mathy kinds of puzzles are very interesting, and this one is much more interesting with the ambiguity of the 1000 clues than if it had just had 8s and 27s as x-sums in a normal way. Great set up for a puzzle, and wonderful solve, Simon. There in the middle of the video, though, you were inviting us to be critical of your solving, and I can't be in favor of that. We may occasionally see a little thing that you missed, but we are not seeing all that you are seeing in the meantime. Whereas there may be many who watch this channel who can solve these puzzles faster than you can, I daresay that few can do so while explaining and demonstrating the logic all the while. For myself, I rarely see anything that you miss that has any significance at all, and my definition of significance is if, had you spotted it, you would have not been stuck. As long as you (or Mark) are making progress and keeping the puzzle moving to some degree, I don't consider you to be a numpty or a prize charley or anything else of that sort. So don't help us criticize you! You are an excellent solve, and a wonderful presenter and explainer, and charming to boot. Thanks so much for this video and this channel. (And for those who are still reading this comment, you are among my favorite people, and I urge you to support the kickstarter if you have not already done so, so that we can get more puzzles and a podcast and some poetry!)

[@davidrattner9]

As always Emily, perfectly summed up and astonishingly written by you!! You are constantly one of my favorite people!! :-)

[@emilywilliams3237]

@@davidrattner9 ohh stop it some more! 🤣😎

[@alantaylor846]

Well said!

[@dicebar_]

For clues outside the grid I like to use the line tool to colour the edge of the cell next to the clue. When combined with traffic light colours - red for unused clues, green for ones that are completely done, and yellow (or orange) for anything in between - it's a relatively easy and intuitive way to keep track of your progress. Excellent solve as always!

[@davidmiller9485]

Base 4 is quaternary. Comp sci did come in handy. Edit: should add here that Base 3 is Ternary. I'm more used to using binary and hex which uses a radix of 16. That means 0-9 plus A-F to make up a 16 numeral system.

[@ananas_anna]

Pretty sure quaternary is also the name of the geological era we’re living in.

[@ichich3978]

Is there a 16*16 Sudoku in HEXADEZIMAL? 1 to 9 and A to F in every box row and colum?

[@davidmiller9485]

@@ichich3978 I'm not sure. I was just pointing out that as a programmer of the 80's I'm more used to using hex and assembly when dealing with base numeral systems.

[@falloutfan2502]

Good puzzle, excellent solve as usual. As a stickler, I didn't like the overlook of Base-1, though. 1x1^3 = 1, which is a valid "1000" and Sudoku digit.

[@ennoderksen5402]

Base 1 doesn’t exist. It would only have a single digit, i.e zero.

[@brenthoskisson6979]

Base 1 is also known as boolean - it is either 0 or infinity. The reason is that no base contains its number. (Base 2 doesn't have a 2, Base 3 doesn't have a 3 and Base 10 doesn't have a ? - we represent it as a 1 and 0 together.) So Base 1 goes all the way from 0 to infinity with nothing in between. This, of course, ignores quantum theory which is a theory all about base 1 having something in between it.

[@falloutfan2502]

@@ennoderksen5402 Bases are raised to sequential exponents to give digits. A Base-1 would simply be a 1 or 0, times 1^n, which is always 1. So there's nothing that says it can't exist, and that "1000" cannot be 1. Granted, it's not a useful base, pragmatically speaking, but neither is Base-3. (except to sloths?) :)

[@0LoneTech]

@@falloutfan2502 Unary numbers exist, e.g. roman numerals 1 through 3, but they're not a base system. There are N different digits in an integer base N system, and if you set N=1, you get no different values. Base-1 could only hold the value 0 of arbitrarily selected width, a value which is not a valid sudoku digit. A more interesting thought is the non-integer bases; e.g. base cube root of X would actually make 1000=X, and could represent several irrational numbers using finite numbers of digits.

[@misterdubsteppa]

Just a small info that makes life easier dealing with different based systems: Look at the number counting the digits from right to left. So giving the one's digit on the right the index 1, next the index 2 (with base 10 the ten's digit), next index 3 (with base 10 the hundred's digit) and so on. The value of a single digit in any system with base b is equal to b to the power of its index minus 1. So in this case for 1000 you just have to look at b^3 , cause the only digit that adds its value to the overall number is the fourth. So binary: 2^3 = 8 Or ternary: 3^3 = 27 But quaterny: 4^3 = 64, hence above any valid sudoku sum. Just for reference with base 10: 10^3 = 1000. So a thousandy which is what we are trained to read on sight, which is why it may feel dump to compute, but it shows the actual underlying idea of our number system. The overall value of the number is the sum of the digits values multiplied by the number standing at that digits place.

[@dariobarisic3502]

You have a typo, 4^3 is 64.

[@misterdubsteppa]

@@dariobarisic3502 oh yeah thanks :D

[@johnsouza4391]

At first, I thought this was a silly puzzle. But once the 1000 clues reduced to either 8 or 27, the solve hooked me. I think it was the minimalism of the clues that made it continually interesting. Thx.

[@VeritasUnae]

I saw how some of the logic might be teased out from the base restrictions and then realising how the x-subs were restricted kept me going. It was just shy of 70 minutes this morning (subtracting a few distraction seconds) but this is just a sublime, enjoyable solve. I love how it also stays tough right to the end with the scouting for the one square which undoes the end. What a beautiful puzzle, Christoph! And well solved Simon c:

[@VeritasUnae]

(Probably the longest solve I’ve attempted in a while too!)

[@jamesdonnelly9217]

"I got distracted by my brain". I'm going to start using that to explain away all sorts of things :)

[@emilywilliams3237]

Isn't that a wonderful expression? I am sure it would be very useful in my life, as well.

[@th.nd.r]

Brilliant puzzle! The fact that such a bare-bones setup can lead to such a wonderful solve path is incredible. Great setting and solving. The names for the first several bases: unary, binary, ternary, quaternary, quinary, senary, septenary, octal, nonary, decimal, undecimal, duodecimal, tridecimal, tetradecimal, pentadecimal, hexadecimal, heptadecimal, octodecimal, enneadecimal, vigesimal, unvigesimal … now going by tens, trigesimal, quadragesimal, quinquagesimal, sexagesimal, septuagesimal, octogesimal, nonagesimal, centesimal. Favorite quote from today’s video: - “Let me explain what a number base is. Basically, - basically[…]”

[@chocolateboy300]

I finished in 81 minutes. This was such a cool idea for a puzzle. These are the kinds of things I love, creative and enjoyable. I'm very behind on my base numbers ability, so I had to manually write them out. I knew I could just look them up, but I figured it would be very limited anyway and did it by hand. I just realized now looking at the pattern, I could have just cubed the base number and got my answer very quickly. At least I know that now. The rest was very fun to figure out. I think my favorite part was deciding where 4 went in row 9. It was surprisingly limited in a fun way. I liked this one very much. Great Puzzle!

[@joubess]

Great puzzle, Simon!!! Having to combine bases 2 and 3 and figuring out which clue is 8 and which is 27 was amazing fun! The 8s that went into the clues inside the grid helped with that immensely. Then all those clues at the bottom left had to be different totals given Sudoku constraints. We just had to figure out which was which!!!. That was fun. I finished in 43:58, but I couldn't break in until you explained counting in bases 2 and 3 because I had forgotten how to do it! Counting in bases other than 10 are difficult for me. I'm not in computer science, and my only use for bases has been in logarithms using tables or a calculator. I was never taught how to count in other bases.

[@robinisomaa]

43:03. What a work of genius! It looks intimidating, but when you remember how bases work, you realize that there are only two possible bases, each with distinct possibilities for X.

[@forsidious]

Definitely appreciate you walking through how to get 1000 in the different bases. They break my brain normally and that really helped me conceptualize things

[@AlRoderick]

The little story about the aliens is cute but effectively this would be the same puzzle if all you said was say any clue given is a fourth power, the same two answers would be valid because effectively that's what 1,000 means it's base to the fourth power. So an alternate name for the puzzle could be "perfect hypercube", which also sounds like something invented by aliens.

[@chrishawkins963]

while perfect hypercubes are certainly alien, we're looking at perfect cubes here unfortunately.

[@AlRoderick]

@@chrishawkins963 Yeah I forgot that the ones place is the zeroith power.

[@RickyWallace]

55 minutes. Proud of that solve, thanks to the training from CtC! Excellent puzzle

[@RichSmith77]

I reckon I could be a master at sudoku on the planet where the aliens use base 2. "Place the digit 1 in this 1x1 grid so that no digit repeats in any row or column". I wouldn't even need any givens.

[@alanclarke4646]

Be my fastest solve ever!😁

[@RichSmith77]

@@alanclarke4646 "I know how to slow you down I'll make it a fog of war puzzle. Woah Ha Ha Ha!!!... Oh, you've finished."

[@alanclarke4646]

@@RichSmith77 😁😁 I rather enjoyed the last fog of war puzzle on here!

[@RicardoRibeiro1978]

At first I thought this puzzle would be too difficult and I wasn't even going to try. But then reading through the rules I thought I would give it a try but ended up getting stuck because in my mind the entire X Sum clue should be in the same base. Meaning, for example, in row 1 the 1000 clue outside the grid should be in the same base as the 1000 in R1C3. With that in mind, I thought I was off to a good start but of course immediately bumped into column 9. To me it didn't make sense that you'd have a base outside the grid and then a different base in that row/column because those are part of the same clue. I'm mostly disappointed at myself but every now and then there are these rules that I find misleading and end up spoiling the experience.

[@multipleofzero4724]

This puzzle looks sweet, excited to watch this solve. Also, for anyone interested in place value and number bases, I highly recommend James Tantum's Exploding Dots series

[@markwizy4661]

When my wife turned 40 we threw her a 28th birthday party because 28 in hexidecimal is 40 in base 10.

[@ericpraline1302]

Some lovely steps in this puzzle, as one would expect from Christoph.

[@amoswittenbergsmusings]

Many sistern and brethren wonder about base 1. Someone suggested that 1000 in base one could be 4. This is not right. 1000 is always equal to the base raised to the 3rd power and 1^3 still is 1. Base 1 crossed my mind as well. In the finite field {0,1} it would be possible. All numbers that are not 0 are equal to 1 in that field. I think this particular field is usually called the trivial finite field. Allowing this seemingly useless field can come in handy - it admits trivial solutions to problems, often a crucial step in a proof. Since in this field 1+1=0, any string of 0s and 1s interpreted in base 1 would equal 0 for an even number of 1s and equal to 1 for odd numbers of 1s. Someone may object that 1 is not a digit in base 1 and that is true but one can allow a value of base and even higher than base to take a place in the n-ary number, not a very useful notion but not strictly forbidden, depending on one's definition of an n-ary notation. Mathematics weirds the mind.

[@sirploko]

Who are You, Who are so Wise in the Ways of Science?

[@amoswittenbergsmusings]

@@sirploko Aw shucks... Just a maths geek.

[@0LoneTech]

Actually, higher digits is a useful notion. We use it in e.g. carry-save adders, which allow a large number of numbers to be summed with very short carry chains. But in contrast to the base 1 concept, those are still numbers that *have* a binary representation, they just haven't resolved to it while their carry component is non-zero.

[@praematura]

37:42 for me, what an amazing puzzle! I honestly didn't think I'd be able to solve it, but was willing to give it a go, and I was glad I did!

[@HunterJE]

Since we’re talking bases, why did the mathematician confuse Christmas with Halloween? … … … Because 25 Dec*= 31 Oct** *-imal **-al

[@HunterJE]

Also base four is called “quaternary”

[@Wecoc1]

There are two types of person, those who know octal and those who don't

[@Wecoc1]

Wait, I messed this up

[@bobblebardsley]

@@Wecoc1 Get in the bin* *-ary

[@ragnkja]

@@Wecoc1 There are 10 types of people: those who understand hexadecimal, and F the rest.

[@dustinkeier9176]

At 48:57, when you place the 13 pair in row 6, that will delineate your 23 pairs. By ruling both 1 and 3 out of R8C4, R9C4.

[@RichSmith77]

An interesting way to rule out 3 from r1c5 from around 44:00 is to see that you get 314 roping vertically in the central columns that clashes with the 314 in box 6.

[@lawrence6132]

This puzzle is a lot harder if we allow the possibility of Base 1. 1000 in Base 1 is 1^3 = 1, which is both a valid X-SUM clue and Sudoku cell entry. If R9C1=1, the bottom row of clues becomes disconnected. How was Base 1 ruled out?

[@RichSmith77]

I don't believe base-1 is a valid base. 1000 uses two digits, not one. For any base n, you cannot have the digit n appearing in a number in that base. You only have digits 0 to (n-1), so for a hypothetical base 1 you would only have the digit 0.

[@alexion3007]

​@@RichSmith77 I disagree - this is assuming that base 1 would work identically to bases 2 and up, which it clearly shouldn't. Unary numerical systems are existent things (see en.wikipedia.org/wiki/Unary_numeral_system ) and as such should have been considered. Now, your point of there being two symbols is reasonable - however, I would argue that were I to be an alien with a unary number system, the position of the tallies might have become a form of artistic expression. And it is not unreasonable for there to be a filler indicator to help further these expressions, and as such construct quite reasonably 1 = 1000.

[@Umbra451]

51:24 another way to look at this one is that the cells sum up to 22, which is an even number. Therefore, it either has four odd digits (1-5-7-9, which is not an option thanks to R8C9) or it has two odd digits and two even digits. Checking the possibilities for the even digits shows that 4 and 8 is the only option that works.

[@groovinhooves]

In standard notation, whatever the base, digits in their columns represent that count of the base integer raised to count of the column minus one (because the units digit, regardless of base is the power zero column - oh, and remember we distribute exponents before simple multiplication, right?). It's really that simple.

[@henk-ottolimburg7947]

You might calculate (and explain) it with powers. In the decimal numbering, the last digit represents units, or 10^0. The 2nd digit from right represents tenths, or 10 ^1, etc. it's the same with any other number base, lets say 3 the last = units the second last = 3^1, so 3. the third last nuber represents 3^2, so 9 the fourth last number (which is the first here) represeents 3^3 , so 27.

[@guilded0n3]

Base 2 is binary. Base 3 is trinary. Base 4 is quaternary. Base 5 is quintary. Base 6 is sexternary I think. Base 7 is septernary I think. Base 8 is octonary I think. Base 9 is notary I think. All bases are x^0 =1, x^1= 10, x^2=100 and x^3=1000 for an easy way to find the places you add the next digit.

[@yoshi6421]

Base 9 I believe is nonary. The Nonary Games said so...

[@vincet68]

This is a great puzzle - challenging but still approachable.

[@Harry-qq2ww]

Fun puzzle! We were stuck in the beginning because we had base 1 as a possibility... took watching Simon's explanation and first 8s to eliminate that.

[@annae933]

thanks simon! the longhand explanation of tenary is the first explanation of alternative base systems that i've actually understood lol

[@HowManyRobot]

In 'base 10'/decimal, each 'place' represents a different power of 10. Starting at the right, the first 'place' is the number of 10^0s (ones), then one spot to the left is the number of 10^1s (tens), then number of 10^2s (hundreds), then the number of 10^3s (thousands). So the number 1234 is (1 * 1000) + (2 * 100) + (3 * 10) + (4 * 1). As a consequence, it's also the number of different digits (including zero) that you must use to represent each 'place'. 0,1,2,3,4,5,6,7,8,9 is ten different digits. It's the same in all bases. e.g. 134 in base 8, converted to decimal, (1 * 8^2) + (3 * 8^1) + (4 * 8^0) --aka--> (1 * 64) + (3 * 8) + (4 * 1) --aka--> (64 + 24 + 4) --aka--> 92 If you go above base 10 you need to invent characters to stand in for single digits larger than 9, which is why base 16/hexadecimal uses A to mean 10, B to mean 11, etc. e.g. A31F in base 16, converted to decimal, (10 * 16^3) + (3 * 16^ 2) + (1 * 16^1) + (15 * 16^0) --aka--> (10 * 4096) + (3 * 256) + (1 * 16) + (15 * 1) --aka--> (40960 + 768 + 16 + 15) --aka--> 41759

[@HowManyRobot]

And, of course, to go the other way, decimal to base x, you'd divide the number by the highest power of x that is smaller than the number, then divide the remainder by the next smallest power of x, etc. Also yes anything raised to the power of zero is 1 for some reason.

[@aksp8727]

47:52 I didn't directly make up the 4 numbers to 22 in the column 3 x-sum area. Insteadly, I discovered that when combining the 4-6-5 x-sum area from the buttom in column 1-2-3, that's an area including the entire box 7 and additional 6 cells in box 4 with a sum of 81. Apart from the entire box 7, which is added up to 45, and r4c1+r5c1=9, the rest is 4 cells that's added up to 27 including a 6. So the 3 numbers need to add up to 21. That can only be 489 because the 4 cells have already had a 6 and all of the rest 3 are looked at by 5s.

[@LinaSavos]

The reason I don't like being early to CTC videos is that there's not enough gold in the comments yet

[@amoswittenbergsmusings]

+1 The quality of the comments is remarkably high.

[@Swisswavey]

I nearly didn't even try this one. I thought it looked too difficult. I'm so glad I did. It's a great puzzle and wasn't as hard as I imagined. The aliens are welcome here!

[@iabervon]

Solved it in 58:25, and I was surprised to find I'd nearly matched Simon's time, until I looked at how much of the video was explaining what the instructions meant.

[@Kris_not_Chris]

hello, someone here: Base 3 = Ternary Base 4 = Quaternary (I've heard it as Quarnary too) Base 5 = Quinary Base 6 = Senary Base 7 = Septenary (I think it should be Heptal, because that sounds better) Base 8 = Octal Base 9 = Nonary Base 10 = Decimal Base 12 = Duodecimal (sometimes called Dozenal) Base 16 = Hexadecimal Base 20 = Vigesimal

[@alexion3007]

Important - Base 1 is not considered. I've managed to find another solution to this puzzle that allows base 1 to be a valid base for the Aliens (which, to be clear, is within the realm of reason. One can consider base 1 to be effectively tallymarks, and that's something that is actually used). This is something that initially made me struggle when doing the sudoku, until I checked the video and noticed that Simon didn't consider it.

[@alexion3007]

A solution that works for base 1, for example, is as follows: 6 2 8 | 3 1 7 | 4 9 5 4 1 7 | 8 5 9 | 2 3 6 5 9 3 | 4 2 6 | 7 1 8 - - - - - - - - - - - - - 2 6 5 | 1 3 4 | 9 8 7 3 4 9 | 5 7 8 | 6 2 1 7 8 1 | 9 6 2 | 3 5 4 - - - - - - - - - - - - - 9 3 4 | 7 8 1 | 5 6 2 8 7 2 | 6 9 5 | 1 4 3 1 5 6 | 2 4 3 | 8 7 9 One can note that there are 3 xsums who sum to 1 (bottom left, middle top, middle right).

[@doughmcn]

I made this puzzle way harder than it actually was by considering Base1 as an option.

[@alittlelifeofmel5157]

I’ve been a silent watcher for a long time now because I’m a horrible sudoku solver. I struggle with easy normal sudoku puzzles, but I’ve surprised myself watching sometimes in that I’m able to spot some digits before you both! But this puzzle has truly bamboozled me to my core. I don’t even know if it was in English half the time 😂 Remarkable feat figuring this one out and solving it!

[@wayneblackburn9645]

Also found this enjoyable and less difficult than it looked - about the right level for me really without needing fancy set theory, x-wings etc.

[@Orenotter]

How goofy those aliens were. They made the whole grid seem unsure. For the the number 1K Acted in a strange way 'Twas to Simon no fright, but a lure.

[@emilywilliams3237]

Perfect.

[@wariolandgoldpiramid]

this was wonderful

[@francoistrempe]

Quick comment about number bases and their names. Decimal should not be named base 10, because this assumes that the 10 in question is in decimal. Using that logic all bases are base 10 (as 2 in binary is 10, or 8 in octal is 10, etc...). Decimal should therefore be called Base A (which is the number after 9 in the next highest base), and Hexadecimal should be called Base G and not 16 (which would also be the number after F in the next highest base).

[@0LoneTech]

Why would those letter names be better? The definitions you're using are reliant on the number of digits before switching over to an alphabet (and its arbitrary order), which is exactly the information you were implying was too vague, but then omitted entirely. Meanwhile, binary, ternary, quaternary, octal, decimal and hexadecimal use established and defined names for the values (mostly in latin). Even "base 10" makes sense as the base of the phrase is defined by context; it's just not new information.

[@francoistrempe]

@@0LoneTech the bases before decimal are all represented by a digit that does not exist in their base. For example, base 2 for binary where 2 is 10 in that base, base 8 for octal where 8 is 10 in that base. Using the same logic decimal should be called by the number in any higher base that would represent 10 in that base. Since Hex uses A as the digit after 9, that should be the base number for decimal.

[@0LoneTech]

@@francoistrempe They're indicated by a number, which is the number used as a base in an exponentiation. We have these bases specifically to not deal with infinite arbitrary symbols for every possible value. For instance, insisting all bases must be written in base >N wouldn't be very intuitive when discussing base 58 vs base 128 (yes, both are in use). In particular, base 58 is used *because* it doesn't have the same digit order as base 62 (it omits some easily confused digits).

[@StephenMarkTurner]

1000 is 'base cubed'. base 2 = 8, base 3 = 27, base 4 = 64 ...

[@PeterJavi]

That's very cool, but why is this and where does it break?

[@ragnkja]

@@PeterJavi 1000 = 10*10*10 = 10^3, no matter what base you’re using (although in the two smallest integer bases, binary and ternary, the “3” in the exponent would be written as “11” and “10” respectively).

[@zmaj12321]

@@PeterJavi It never breaks. For example, in base 10, the numbers 1, 10, 100, ... are the powers of 10. The same thing happens in any base. You can relate this to how Simon explained bases. Let's count in base b. After putting b-1 in the ones place, the next number is b. We need a new digit, so we set 10 to equal b. Every b steps, we will reset the ones digit to zero and increase the next place by 1. After we do this b times, we will reach the value b*b=b^2, but we can't use b as a digit, so we need a third digit and we set 100 to equal b^2. Now, we need to increase the third digit every b^2 steps. After b iterations, we reach the value b*b^2=b^3 and we need 4 digits, so b^3 is 1000.

[@rikki1954]

@@zmaj12321 As an aside any base to the power 0 is 1, therefore 2^0=1, 3^0=1 and so on.

[@longwaytotipperary]

Can you extend the kickstarter to get to the levels where Simon reads poetry & we get a CTC podcast? 🤔

[@confusedSoulof2010]

The poetry needed 180k which we've surpassed and the CTC podcast season 2 needs $191,302... we are currently, as I type this, backed to exactly $191,302.

[@longwaytotipperary]

@@confusedSoulof2010 I just went to the kickstarter link in the description and it only shows $178,108. I hope you have better info - that would be spectacular!!

[@bethelliot7140]

It is saying over $182,000 for me as of writing this 👍🤗

[@longwaytotipperary]

@@bethelliot7140 so we get Simon reading poetry - yay!! 😃

[@listey]

@@longwaytotipperary $ are worth different amounts in different countries.

[@amoswittenbergsmusings]

33:28 R1C9 cannot be a 6 - the outies would have to sum to 18, putting a 5 in R1C2 which cannot be. [edit] And a few seconds later Simon used C9 outies to reach the same conclusion. Still, I pat myself on the back. I am grateful for the tiniest insights I reach before the master. 42:44 R9C4 cannot be a 4 because that would need a 6/8/9 triple above it and R1C4 rules it out. Now we have a 2/3 pair in R9C4C5 and a 4/5 pair in R9C2C3. R9C4 cannot be a 4 because of the 8 in R1, so R9C2 is 4 and R9C3 is 5. I am by now positively glowing with childish pride. [edit] 43:40 Simon also sees it!

[@emilywilliams3237]

I love your description of this! Sometime people commenting on things that Simon fails to see or sees in a different way is very annoying to me, but your comments are absolutely fabulous and very charming and kind - and funny! Thanks for sharing!

[@amoswittenbergsmusings]

@@emilywilliams3237 Now I can go to sleep in the secure knowledge that at least I have not done too much harm today ;-) In general, the tone of the comments on the channel is benign, I think. I mean, Simon always mentions that he appreciates *kind* comments. The least we watchers can do is to reciprocate Simon's unfailing goodness.

[@emilywilliams3237]

@@amoswittenbergsmusings Well said!

[@wanderlustwarrior]

1:39:04 for me and I needed a little bit of help from the video. I like these base puzzles, but didn't do well on this one.

[@BryanLu0]

If people watch through the entire video, long videos are actually better, because you get more watch time out of it

[@Vanziethel]

47:50 Is that deduction valid? Wouldn't 5+2+3+8+9 and 5+3+4+7+8 have worked as well? Why did you need the nines?

[@RichSmith77]

8 isn't available. Already placed at the top of the column.

[@Vanziethel]

@@RichSmith77 Thanks, not sure why I didn't notice that

[@samhitchcock3560]

Actually, coming back to this: the 8 is used in box 1 already, so nothing with 8 works for that clue. And when he says 5+3+4+7+9 and reducing only one, he must put 4 and 9 in box 4 and 2 and 7 in box 7. Earlier today, I thought I saw an alternative of putting 4 on box 7 but apparently I wasn't very attentative..

[@wariolandgoldpiramid]

15:25 well, that was a brilliant introduction.

[@complainer406]

Why don't the rules describe the 1000s in the grid?

[@michaeldew7904]

They do. The only number that works in any base that allows 4 digits is base 2.

[@omriorgad7771]

@@michaeldew7904 But they don't say 'these are given numbers'

[@michaeldew7904]

@@omriorgad7771 The only single digit number that can be represented by 1000 is in base 2 and that number is 8. It's the only answer it can be.

[@thundermill7109]

It’s like a pencil mark in the grid. Doesn’t need to be described by rules.

[@crystalgehrt8861]

I often have trouble with x-sums because I keep forgetting what the number on the outside does vs the first digit and I keep making mistakes, so I actually found this one easier because I wasn't looking at the numbers on the outside. haha

[@kathyjohnson2043]

I think Rocky, the US math teacher Sudoku setter, should share this one with his students. (Rocky, if I've remembered your name incorrectly, I sincerely apologize...as a retired teacher, there are just too many names stuck in my head. And, if anyone else realizes I've remembered incorrectly, please chime in to help me.)

[@Coyotek4]

42:38 ... I was *slow* on this one (took me 10 minutes just to realize I couldn't use Base 1, then forgot that an X-sum '4' clue only had one possibility for completing the sum), but I did eventually get there. Nice puzzle!

[@RichSmith77]

An x-sum clue of 4 isn't possible. 4 in a base-1 (If it existed) would surely be 1111, not 1000.

[@Coyotek4]

@@RichSmith77 By '4' clue, I mean a row/column beginning with 4 ... such a row/column must have an X-sum of 27 and have the digits 6,8,9 as the other numbers.

[@RichSmith77]

@@Coyotek4 Oops. Sorry. Think I was influenced by reading other comments saying 1000 could be 4 in base-1. My bad.

[@lawrence6132]

How did you rule out Base 1? Technically, 1000 in base 1 is 1x1^3 + 0x1^2 + 0x1^1 + 0x1^0 = 1, and 1 is a valid X-sum as well as Sudoku cell entry.

[@RichSmith77]

@@lawrence6132 You cannot use digit 'n' in base-n. So just like you cannot use digit 2 when writing binary numbers, you cannot use digit 1 when writing base-1 numbers. The only digit you have is 0, which cannot be used to express any number other than 0. Base-1 isn't a thing. (You might have something similar base-1 if you only allowed yourself to express numbers with a 1, so 1=1, 11=2, 111=3, etc. But in this system, 1000 wouldn't be permitted as it it uses two digits, and unlike any other base, you would have no way to write 0.)

[@Seehart]

The clues could be anything! For example, Andorians happen to use the cube root of 7 as their base, so at least one of the sums is 7 if any alien is Andorian.

[@RichSmith77]

I'd be fascinated to learn the history of the Andorians. What was the reason they picked the cube root of 7 as their base for counting? I imagine it gave their early barterers and store keepers a terrible time. 😂

[@Seehart]

@@RichSmith77 I tried to get some help from OpenAI....The following is a conversation with an AI assistant. The assistant is helpful, creative, clever, and very friendly. Human: Hello, who are you? AI: I am an AI created by OpenAI. How can I help you today? Human: Why do Andorians use the cube root of 7 as their counting base? AI: Andorians use the cube root of 7 as their counting base because it is a more efficient way to count. When using the cube root of 7, Andorians can count faster and more accurately than if they were to use another counting base. Human: The cube root of 7 is irrational. For humans, this makes it difficult to use for counting. What aspect of Andorian culture makes use of an irrational number such as the cube root of 7 ideal for counting? AI: Andorians have a strong sense of logic and order, which makes the use of an irrational number such as the cube root of 7 ideal for counting. Andorians count by grouping numbers together in threes, which is more efficient than the way humans count. The use of the cube root of 7 allows Andorians to easily keep track of large numbers of objects. Human: Ah, I see. How many fingers to Andorians have? AI: Andorians have four fingers on each hand. Human: Are some of these fingers irrational? That might expain why they use an irrational counting base. AI: No, all of the fingers on an Andorian hand are rational. However, Andorians use the cube root of 7 as their counting base because it is a more efficient way to count. When using the cube root of 7, Andorians can count faster and more accurately than if they were to use another counting base.

[@RichSmith77]

@@Seehart I'm convinced. It's a more efficient way to count. Don't know how I missed it. 😂👏👏👏

[@Seehart]

@@RichSmith77 I set up the context as an expert on this subject matter. This is also interesting: The following is a conversation with an expert AI exobiologist with knowledge of Andorian culture. Human: Hello AI: Hello! Thank you for speaking with me. Human: As you know, Andorians use the cube root of 7 for their counting base. Can you explain why? AI: Andorians use the cube root of 7 for their counting base because it is a sacred number in their culture. It represents the seven elements that make up their world: fire, water, air, earth, metal, wood, and spirit. Human: The cube root of 7 is irrational. For humans, this makes it difficult to use for counting. What aspect of Andorian culture makes use of an irrational number such as the cube root of 7 ideal for counting? AI: Andorians believe that the universe is fundamentally irrational, so they see no problem with using an irrational number like the cube root of 7 for counting. They believe that it actually makes their counting system more accurate, because it better reflects the true nature of reality.

[@RichSmith77]

@@Seehart Irrationally, KZbin does not appear to allow me to give you 'cube root of 7' thumbs up. Disappointing. One will have to suffice. 👍

[@denniskrog3705]

The He-man reference was spot-on 😂

[@jurjenvanderhoek316]

13:42 Base 4 is called quaternary!

[@vidaroni]

@34:30 "By the power of Grayskull... and also sudoku."

[@Rach881101]

46:15 for me. Interesting logic and puzzle!

[@soulshado]

Do you have any puzzles showing ordered distances i just cant understand the rules of puzzle #14 by clover on the app

[@ellaenchanted2399]

Simon: We must be just about the only channel on the internet that enjoys talking about number bases (paraphrased) Numberphile: Are we a joke to you? Fans of Both: We binge for /reasons/ you are aware. 1000 reasons

[@pewterhacker]

Great rule set and reasonably difficult!

[@alexweavers5599]

Thanksgiving is coming up and I'll be so thankful if Simon notices that the logic he applied to the purple cells (subtracting from 45) on the left applies equally to the yellow cells by the end of the video.

[@zergrush8709]

why weren't the given digit clues explained? I didn't understand what those meant at first

[@josephdlist]

If anyone loves bases and number theory, numberfile is a great channel.

[@HunterJE]

The 89 pencil mark at 45:37 is technically placed using a sextuple on 123467, which is not a “tuple” you get to use often!

[@ragnkja]

Every “naked” -tuple has a “hidden” counterpart, and vice versa.

[@HunterJE]

@@ragnkja Yeah, but not often that you have every cell of the sextuple pencil marked before the complementary pair!

[@ueliriegg]

"I got ditracted by my brain". Story of my life :D

[@awilliams1701]

It's over 9000!

[@sonalita_]

@Simon, you’ve still not updated your app banner overlay to include the GAS app…

[@dmytro_shum]

29:05 Can anyone tell me what does Simon mean of "absolute prize Charlie" ?

[@smylesg]

44:00 Biting my nails until now waiting for him to realize r9c3 cannot be 4, even with the given 8 sitting atop the column the entire time.

[@michaelmele3954]

Please let it be known that the KZbin guidance is wrong. Shorter videos are not preferred. KZbin is mistakenly tracking viewers by the number of videos they watch rather than the total watch time. I, for one, prefer to put on a long video while going about my business just to reduce the number of times I need to select a new video.

[@joelstorey]

Simon should mark the completed clues with an X (using Pen Tool) on the border between the clue and the grid

[@jimmahT]

Thanks Simon

[@kimh6979]

More video games please. I’ve watched Overdrive 3 times

[@francoisduez601]

42:57 Nice logic... But overlooking a clue can make a lot of damage timewise 😵

[@kimlethan]

Does this puzzle really have an unique solution? Nowhere is it stated that bases has to natural numbers (they are aliens after all), so you can get any number between 2 and 45 just by using the cube root of that number as base. Hence you can get multiple solutions.

[@RichSmith77]

I don't think it's unreasonable to assume any alien would develop a number system based on a natural number as the base. (Possibly related to their number of fingers, toes or tentacles. Or 60. 😂). I don't see how number systems don't stem from counting things. Fractions, rationals and irrationals will surely only come about after a number system has been developed for the natural numbers. There's a reason they're called "natural numbers" after all. But technically, you're correct. The best kind of correct. 😀

[@xaveruth]

Spent a lot of time thinking base 1 was allowed… 😢

[@Shaltinanwenor]

88:50 I spent waaaaaaay too long wasting time after a logic error in box 7. Probably lost a good ~30 mins to that. Madge.

[@Oscaragious]

I really didn't like the fact that the center 1000 clues were left unexplained. The description never said the aliens wrote those clues, and even if they did, it was not indicated how they applied to the puzzle. Center clues are generally not part of puzzles, and solvers are free to use "pencil marks" in any way they see fit. Center clues at best typically represent an array of possible digits, which never translates to a multi-digit number. Was this puzzle still uniquely solvable without using those center clues?

[@Mer134]

If you happen to give X-men 2 a watch and fast forward to 1:20:54, then Magneto seems to be watching a Cracking the Cryptic video.

[@dutpar]

They’d have been 14 years before the channel started, so would require some serious mutant powers!

[@DanielCathers]

If you had a variant with 100 clues as well, you could call it Hundreds and Thousands.

[@khoozu7802]

38.08 there's gonna never be a 2 because u will have two 6's in that column

[@deerel]

I had the video paused at 18:41. Click play. Every thing is still. Still paused? Click again. Paused. What? Simon is like freeze famed for 6 seconds. 😂

[@randysavage1011]

Quartenary

[@_-_-Sipita-_-_]

25:26 for me. gj for the aliens

[@klacow]

i walked in the wrong room, can someone point me to basic maths class :/

[@Casswaria]

40:34 for me, what a blast!

[@SekGuy]

The rules are missing the fact that the base has to be an integer for this to work. If the base is the cube root of any integer n, then 1000 in that base is n.

[@SekGuy]

This means that if the base is cuberoot of seven, then 1000 would mean seven.

[@RichSmith77]

@@SekGuy I'm struggling to think of a reason why an alien species would develop a number system that didn't use a Natural number as it's base.

[@SekGuy]

@@RichSmith77 hah. good point. but making assumptions about them using Natural numbers as number base is just sloppy.

[@tho63723]

Isn’t 1000 base 1000 equal to 1 a valid option?

[@merkdirwas]

sadly this direction is never meant, its always whatever based number in ordered positions .. not backwards, or at least 1000 has to be the ordered representation, which makes it ridiculy in base1000 = 1000*1000*1000 in base10. the baddy is base 1 , which would make it reasonable a 4.

[@SilverKiMak]

Just realised that Roman Numerals are sort of Base 1 numbers. Albeit with some abbreviations, live a V being short for IIIII, C short for IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII etc... 🤔

[@0LoneTech]

It's more complicated. For one thing, unary tallies aren't base-1 in that bases get digit weights defined by positions counted from the unit position. *All* positions are unit in unary tallies. But that's not the case in Roman numerals; IV has altered the meaning of I because of where it is in relation to V. And we get conventions complicating that further when IIX isn't allowed but VIII is (with more symbols and lines). So Roman numerals are a system of tallies with substitutions, exceptions and exceptions to exceptions. They're hardly alone in making such a mess; Danish and French have other dramatic numbering systems.

[@SilverKiMak]

@@0LoneTech You're right, didn't think of that. I don't want to know what French came up with, if even Romans have so many exceptions to rules )))

[@Fizzfaldt]

14:26 "All of these clues are either 8s or 27s" You discounted base 1 (which is weird) which would mean the clues can also be 1. It's awkward... but allowed by the rules of bases. Though given that you released the video I'm sure you solved it (I'm writing this early) so I'm sure Christoph intended you to ignore base 1

[@bigben0012]

I don't think you can write 1000 in base 1 though. Base 1 implies there is only 1 digit, but "1" and "0" are two different digits.

[@Fizzfaldt]

@@bigben0012 I get why you'd think that, but sometimes base cases don't work that way. Unary (base 1) has two symbols, 0 and 1. And the number represented is just how many 1s you have. (Since 1^n = 1). You're thinking of what looks like a general rule that does work for all bases of positive integers greater than 1. But your rule (n symbols for base n) also doesn't work for any negative bases, nor for non-integer bases.

[@Fizzfaldt]

1000 in unary is 1. 1*1^3+0+0+0