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

@LegendarySkar

4 жыл бұрын

The Parker squared Square Shuffle

@DenisRyan

4 жыл бұрын

Came here to say similar. Well played.

@yvesisnotaname2813

4 жыл бұрын

Denis Ryan The Parker Square Shuffle

@ykl1277

4 жыл бұрын

Parker^2 shuffle

@feronanthus9756

4 жыл бұрын

Defeated or proved?

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

4 жыл бұрын

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

@Tondadrd

4 жыл бұрын

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

@user-ow1bc4sx2r

4 жыл бұрын

This is a much better solution hahahah

@mattsnyder4754

4 жыл бұрын

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

@dan200smx7

4 жыл бұрын

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

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

4 жыл бұрын

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

4 жыл бұрын

@@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

4 жыл бұрын

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

@maxonmendel5757

4 жыл бұрын

@@Skatche why's that?

@_adela

4 жыл бұрын

​@@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.

The Parker Shuffle?

@dan200smx7

4 жыл бұрын

The 10x10 Parker square?

@TheDannyHamilton

4 жыл бұрын

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

@davidmulqueen8322

4 жыл бұрын

The Enoch Root shuffle.

@armofrobot

4 жыл бұрын

That sounds like the new mathematical dance craze!

@MathTchr101

4 жыл бұрын

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

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

@daminox

4 жыл бұрын

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

@michelfug

4 жыл бұрын

Parker poker

@Kram1032

4 жыл бұрын

Porker Paker

The obvious way to play is with quantum entangled scrabble pieces

@RFC3514

4 жыл бұрын

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

@andrewsparkes8829

4 жыл бұрын

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

@RFC3514

4 жыл бұрын

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

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

@gruber3349

4 жыл бұрын

Shoutouts to Germany ;)

@frederickm9823

4 жыл бұрын

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

@asailijhijr

4 жыл бұрын

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

4 жыл бұрын

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

@shaileshrana7165

4 жыл бұрын

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

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.

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

4 жыл бұрын

I think you just (re-)invented Countdown.

@cyrylo23

4 жыл бұрын

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

4 жыл бұрын

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

@ink7761

4 жыл бұрын

This is countdown

@harrybarrow6222

4 жыл бұрын

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

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

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

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

@WMTeWu

4 жыл бұрын

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

@matthewellisor5835

4 жыл бұрын

@@WMTeWu Too soon

@RecursiveTriforce

4 жыл бұрын

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

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

4 жыл бұрын

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

@coolfred9083

4 жыл бұрын

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

@joostvanrens

4 жыл бұрын

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

@user-vn7ce5ig1z

4 жыл бұрын

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

@mattsnyder4754

4 жыл бұрын

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

A Parker Square of Scrabble tiles shuffled to perfection

@nanamacapagal8342

4 жыл бұрын

Perfection.

@nanigopalsaha2408

4 жыл бұрын

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

@asailijhijr

4 жыл бұрын

> Parker Square @@nanamacapagal8342

@Tefans97

4 жыл бұрын

MPMP II the revenge of the squares

@nanamacapagal8342

4 жыл бұрын

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

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

@jackdog06

4 жыл бұрын

bloergk the “y” actually subtracts points

@leeprice133

4 жыл бұрын

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

@leeprice133

4 жыл бұрын

@@rosiefay7283 Ch and Ff as well

@JNCressey

4 жыл бұрын

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

@qwertyTRiG

4 жыл бұрын

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

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

@Iojeka

4 жыл бұрын

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

@georgelionon9050

4 жыл бұрын

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)

“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

4 жыл бұрын

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

4 жыл бұрын

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

@bluerizlagirl

4 жыл бұрын

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

4 жыл бұрын

@@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

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

@TheAnimatorsUnite

4 жыл бұрын

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.

4 жыл бұрын

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

@RoderickEtheria

4 жыл бұрын

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.

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

4 жыл бұрын

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

@philipmiesbauer

4 жыл бұрын

@@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

4 жыл бұрын

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

4 жыл бұрын

• 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

4 жыл бұрын

@@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

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

4 жыл бұрын

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

4 жыл бұрын

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.

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

4 жыл бұрын

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

4 жыл бұрын

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

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."

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

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.

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.

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

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

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.

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

4 жыл бұрын

acidfire68594 that only works with a 2 player game

@KylerGreer

4 жыл бұрын

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

4 жыл бұрын

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

4 жыл бұрын

@@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

4 жыл бұрын

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

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

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

@sayanghosh6996

4 жыл бұрын

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

@SiEffen

4 жыл бұрын

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

4 жыл бұрын

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

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

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

4 жыл бұрын

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

4 жыл бұрын

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

@TheZotmeister

4 жыл бұрын

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

@davidrbarnes81

4 жыл бұрын

Or perhaps you omit that rule in quarantine Scrabble?

@walkerwillingham8599

4 жыл бұрын

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.

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

@SuperSt0ne

4 жыл бұрын

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

I love all the puzzles. very interesting.

My favorite KZread maths guy, Natt Oarker!

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

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

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.

-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)

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

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

@SillyPutty125

4 жыл бұрын

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

4 жыл бұрын

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

Going to try this out!

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.

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..."

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

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.)

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

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

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

Really need this in these days.. #quarantine

Amazing video

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

4 жыл бұрын

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

2 жыл бұрын

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.

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

4 жыл бұрын

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

4 жыл бұрын

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

4 жыл бұрын

@@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)

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.

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

@MateusSFigueiredo

4 жыл бұрын

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

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

4 жыл бұрын

Did your answer kind of resemble a year?

@1Resare

4 жыл бұрын

Mine had three digits

@OlliFritz

4 жыл бұрын

@@SpencerTwiddy well technically yes if the Roman Era counts

@1dgram

4 жыл бұрын

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

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

4 жыл бұрын

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.

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.

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 :)

Matt Larker, I mean Natt Oarker

Geoff looks different in this one.

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

4 жыл бұрын

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.

Could you do a simpler shuffle followed by repeatedly applying some random generator of Z/100Z to determine where the tiles are picked from?

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.

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

Well, that is a Matt Parker square of a shuffle if I've ever seen one

I'm living for Vicki's London Transport Museum merch

17:31 That is how my third dates usually end

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

@shelvacu

4 жыл бұрын

i had the same thought!

@plexluthor

4 жыл бұрын

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

@plexluthor

4 жыл бұрын

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

4 жыл бұрын

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

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!

This honestly sounds like a Multi-Party-Computation problem. Secret-Sharing schemes or Oblivious Transfer could be very useful for this.

Has the solution to this puzzle been published yet?

@amystrauss9597

4 жыл бұрын

That's what I came to ask!

@amystrauss9597

4 жыл бұрын

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.

4 жыл бұрын

@@amystrauss9597 Okay, thank you.

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

@darealpoopster

4 жыл бұрын

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

@esquilax5563

4 жыл бұрын

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

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

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.

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

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

@stephenkamenar

4 жыл бұрын

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

@deathsheir2035

4 жыл бұрын

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

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.

i LOVE Matt Puzzles Math Parker

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

4 жыл бұрын

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

Easy, just get Tabletop simulator

Gosh this is so good Please, how much time did you spend shuffling?

This shuffle has two major security problems: 1. both players know the random numbers (the "keys" for the shuffle). this makes it possible to figure out the final state. 2. either player can easily peek on upcoming letters, or the other players letters. I think a much better solution can be made using commutative crypto tricks. This type of shuffling problem is called "Mental Poker" (see excellent wikipedia page) - and there are several good solutions to it already. en.wikipedia.org/wiki/Mental_poker In mental poker shuffles, both players should end up with decks that are shuffled identically, but the decks are encoded in such a way that a player cannot peek on a card (or letter-tile) without permission from the other players. Typically this is done by one player requesting to draw a tile from the pile, and then receiving keys to decrypt that card from all other players. When playing the card, all other players can verify the decrypted card against an encrypted record of what that player would have drawn. The details get a bit crypto-y, but it's neat stuff and fun reading. Can recommend looking into it :)

@XHappyKillerX

4 жыл бұрын

First sentence on the wikipedia page: "Mental poker is the common name for a set of cryptographic problems that concerns playing a fair game over distance without the need for a trusted third party." Wow, that sounds exactly like what we need!

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

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.

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

4 жыл бұрын

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

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

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.

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!

submitted my answer and hoping for the best, as always :D great series matt

@SpencerTwiddy

4 жыл бұрын

did it look kind of like a year?

@itwasinthispositionerinoag7414

4 жыл бұрын

@@SpencerTwiddy nope the answer i came up with was in the low 100s, i may definitely have worked it out incorrectly though. will be interesting to see the right answer and method of working it out next friday

@SpencerTwiddy

4 жыл бұрын

@@itwasinthispositionerinoag7414 Ah ok, yeah will be interesting. Is your name a reference to the chess channel btw? I love watching his vids

@itwasinthispositionerinoag7414

4 жыл бұрын

@@SpencerTwiddy indeed it is! maybe we can bribe matt into making some chess related maths puzzles

@SpencerTwiddy

4 жыл бұрын

@@itwasinthispositionerinoag7414 Hahaha I would be so down! Maybe collab with James Grime on them too, I know he's done some great stuff on mathy chess puzzles

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

I would keep the arranged grid of the letters, and make the drawing random by throwing 10 sided dice. The first tells your column, the second your row. When your letter is taken, just 'count down' that much in the row (choose your piece with modular aritmethic).

@rubie2

4 жыл бұрын

The problem would be that both players would know the layout of the grid, so it would be much easier to work out what tiles your opponent has

@PeterKerenyi

4 жыл бұрын

@@rubie2 true.

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.

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!)

"You could download an app" OR, you can make a web page that takes out all the tedium of shuffling and instead just picks tiles for the players and then play normally. You have the 10x10 grid with the letters up and use them as the physical representation. The problem isn't how to play over a video conference. The problem is that the shunts and shuffles are too error prone.

After the shuffle you could pick a random number from 1 to 100 (first 2 digits of that thing in the Calculator?) and that's the tile you draw so even if you keep track of where some tiles are, you can't do anything about it.

Vicki seems like such a lovely person. 😊

That's why I love Matt Parker videos. Because he'll upload it even when he completely botches it. Parker Shuffle it is. Personally I think one player could show the pieces to the opposing player with out looking it.

Fisher-Yates shuffle algorithm seems to be less busy-work, although some tiles can be traced better. Sattolo's algorithm might work better in that sense with tradeoff for less random.