SOLUTION: Three Indistinguishable Dice Puzzle
ฝัง
- เผยแพร่เมื่อ 7 มิ.ย. 2024
- This video contains a lot of solutions and a lot of dice. Original puzzle suggested by Lucas Garron.
Dice are: ALL GONE
Matt’s online mathematical toys store.
mathsgear.co.uk/
My favourite solution was: Hagen von Eitzen geometric solution.
• Two Dice from Three Dice
Download the Three Dice Hexagon Rolling Guide.
www.dropbox.com/s/dalyidbnzrl...
Original Three Indistinguishable Dice Puzzle video.
• The Three Indistinguis...
Discussion on reddit /r/math
/ 4eltj8
Discussion on the /r/mattparker subreddit.
/ 4ek9ow
Matt Stuart response video.
• The Three Indistinguis...
MrBoxinaboxinabox and Alex youtube comments.
• The Three Indistinguis...
Tarim, solution in a tweet.
/ 719939463707803649
Katie and Paul's "dead easy" solution.
• Dice Puzzle - Katie an...
Marty Wollner video (3 of 3).
• Video
Marty Wollner long description.
spikersystems.com/FlashNet_Poi...
Marty Wollner patent.
www.google.com/patents/US8246446
mathAHA closed formula.
• The Three Indistinguis...
Jan Van Lent python code.
www.dropbox.com/s/cnqh59oq0mg...
CORRECTIONS:
The individual dice values do matter in Monopoly as you roll again on a double. First noticed by Suzie Brown. I though that was a 'house rule' but it's an official rule. You also can roll a double to escape jail.
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/ - บันเทิง
“Hey, does anyone have a couple 6 sided dice handy?”
“No, but I do have three dice sealed in a box and a printed out hexagon if that will work?”
I used to have large, hollow, transparent d6's with a miniature d6 within each. Don't know what happened to them.
@@BolasMinion same here, I also have 3 distinguishable dice in a cube (as opposed to 3 indistinguishable dice in a cube) as well as a couple sets of the "full" dice array (by ttrpg standards at least)
You inadvertently solved it!!! simply glue a dice in the corner, and then ignore it! problem solved!
lol
As was said earlier, "no physical solutions allowed."
A dice?
you mean a die?
A parker square of a solution!
+Broken Wave no. Singular dice is also correct and to many people sounds better.
My brain exploded when you plucked the hexagon off of the screen.
+LittleMikey _head asplode_
+LittleMikey Your head exploded‽ Imagine how I felt!
standupmaths Nah just my brain. Thankfully my skull contained the mess.
+Popcornio Strong Bad!
+LittleMikey Are you still alive?
"Turns out, simulating 1 from 27 is trivial." Brilliant :)
+Penny Lane Indeed. That's the best Parker's Square I've ever seen.
*rolls* ...five
*rolls again*
*the dice fall everywhere*
...three
For a few brief seconds he became an engineer.
@@markenangel1813 I died.
I'm so sad I can't ask a friend to watch twenty minutes of maths videos just to share that one moment of laughter with me. But I'm glad some folks on the internet enjoyed it with four years of time gap !
10:35
Gluing one of the dice to the corner;
most elegant solution
After you roll, flat spin the cube so that the three smaller dice move to the corners. Add the two that end up in opposite corners for a two dice solution. Ignore the two in opposing corners for a one die solution.
Cyanoacrylate adhesives are really hard to use on acrylic without clouding generally, and this was the perfect storm of conditions for that to happen because one of the main ways they cloud (in addition to just incautious application beyond the joint) is blooming, where the C-A monomers evaporate and then deposit on surfaces - since the inside of the cube was completely unventilated the monomers had nowhere else to disperse and so anything that evaporated inside the joint deposited back on the nice clear acrylic...
"Well I can confirm it actually took me..."
*Video ends*
GODDAMMIT MATT!
>Rolls big die
>Explodes on table
"..........Three!!"
Didn't he ask for a math solution?
You're providing a physics solution.
That's not what Shadowrun meant by exploding dice.
That Parker cube quote was priceless
He has submitted to his fate. Loving it. Parker cube ftw!
He said he didn’t want to name the Parker Square because he knew this would happen.
Okay. I admit it. When you grabbed the graphic, that was awesome.
+Teddy Boragina I'm disproportionately proud of that.
You should be
+standupmaths I wish TH-cam made frame scrubbing easier, so I could see the frame where you cut. As far as I can tell without that, you just had your hand perfect.
I think it was hanging behind the graphic and there was no cut.
satisfiction What was it hanging on?
Now we need a bigger dice that contains 3 dies which have 3 dies inside.
+StereoBucket soo meta
and figure out how to take the three indistinguishable pairs of simulated distinguishable dice we can get from that to then simulate three distinguishable dice
you don't seem to understand how the words die and dice work...
Die is singular.
Dice is plural.
Dies isn't an applicable word.
so there you go.
+Broken Wave Ikr
Yo dawg, I heard you like dice...
I can't even imagine the amount of time editing this took. It was all spot on. This channel deserves all the views and then some. I'm a fairly new sub, but I already love this community, and the engaging conversation that is somehow able to take place in the comments. I'm already looking forward to the next puzzle.
The rules to the hexagon method should be on the backside.
loved the last seconds.
Seems like the answer begins with a three.
+Michael Schmitz it may be "13xx", or he wanted to say "3xy" times, so the resoult can be from 3xy*1 to 3xy*9. So, don't rely on that beginning "th" (or at least, I hope it is different from that because I would have got the wrong answer ;_;)
You stopped fighting.
You accepted your legacy.
Your resistance was a classic #ParkerSquare, and it was brilliant.
Thanks for the Parker Cube quote.
+Melody Williams "Parker, the (almost) Great Mathemagician!"
That hexagon solution was brilliant.
Straight to the point
„simulating one from 27 is trivial“ - rolls mother of all dice hahahaha
+Cr42yguy Aaaaaaaa... Three. xD
The shear amount of gusto with which he says, "5!" Is just fantastic.
@@AngryArmadillo but he never said 120
me "Teacher, when am i ever going to use this in real life?"
teacher "if you ever have too much time on your hands and want to make a popular youtube channel"
This kind of dedicated community involvement is something we need more of these days. Thank you! Keep up the good work!
BTW, I loved the 10x10 Parker Grid :)
+Antonio Barba
good one xD
+Antonio Barba cute!
Mathematician: Here's my algorithm for mapping 3 indistinguishable dice to 2 distinguishable dice.
Engineer: Roll the cube then jostle them onto the edge, read the first two dice left to right.
That was my thought too
or just roll it twice
Matt Parker! In addition to your obvious numeracy and charm, you're a KILLER video editor / graphics creator. The time and attention it must take to make the extremely helpful animations that pepper your videos is not lost on me - I'm impressed. Thank you!
Daaahhhhhhhh! You scoundrel, leaving us on a cliffhanger!
+bdot02 Now ask yourself why he specifically showed the dice labeled "9, 7" and "6, 2".
+Cristi Neagu I am too stupid to understand ;-;
+bdot02 Video length is 28:35 for a reason.
well 9,7 is the last dice.
The simplest solution: use the one dice solution, twice.
That acrylic cube assembly job really turned out to be a bit of a Parker square.
True
He made that joke in the video.
*cube
jgallantyt uh oh. Somebody didn't watch all of the video before commenting
Those two videos of yours and the responses they caused are the reason I subscribed.
A very worthy puzzle, and it produced a lot of interesting stuff. Congratulations.
For the 2 dice simulation, couldn't you just role the 3 dice cube 2 times and use the 1 dice simulation? That seems like the simple answer to me.
Lost it when he said parker cube.
+Marcel Robitaille
Parker cube confirmed.
Parabolati Confirmed.
Parker Cube and Parabolati start with the same letter.
Coincidence?
I think not!
The parker cube is infinitely many parker squares stacked, so it must be an even bigger fail than the parker square
vg fabi An infinitely bigger one. There's probably a definition for how much more of a fail it is.
since when did parker squares turn into parker cubes?
+Agent M The glue made it a parker square cube ;)
+Agent M 10/10 bought the shirt
Amr Idrees it's the parker square cube law
parker hypercubes, coming soon to a dimension near you
Misterlegoboy but I can't see 4D
So much crazy math and convoluted solutions, heh. Even the simplest one is pretty crazy. You've got a way to map them to a single dice, right?
Roll it twice.
We choose to -go to the Moon- figure out these puzzles in this decade and do the other things, not because they are easy, but because they are hard.
+logicalfundy That wasn't the puzzle.
If you can change a puzzle it most likely becomes way more easy to solve.
Also those crazy math and convoluted solutions, as you call them, are (at least for me) fun and way more interesting if you are in a group (of math-interest people).
+logicalfundy Roll it twice?! If you're going to cheat, at least cheat efficiently! Label each side of the outer cube 1 to 6 to get a second die in one roll.
In the original video, he said a way to count 3 dice as 1, and that is to take the sum%6 (remainder when sum is divided by 6). In the case when you get 0, treat it as 6.
logicalfundy lol, as if he didn't make it very clear that wasn't allowed xD
I love the transitions, I love the physical hexagon, and I mostly love the ending
21:38 wow
+mark van dijken Thank you. Very proud.
+standupmaths that cut at the end
+standupmaths first the magic lemons, now this Magic Parkergon?
Even at 0.25 speed it's impressive how you made that work!
I hoped when signing them you used a permanent marker.
Matt; "Yes: it'll always be a marker."
Thank you for taking the time and effort to making these videos. It's a joy watching them. Thank you.
Another Monopoly error: You do need to know the individual dice because otherwise, you wouldn't know when you've rolled a double.
But you don't need two distinguishable dice.
This is so simple. Just exclude the one you glued to the corner.
Loved the Parker cube joke :D
POV: you watch the original question the moment it releases, search for solution and find none.
Then forget about it for a long time.
*6 Years later, youtube recommends you the solution*
well I would've just thrown the dice twice
I almost flipped my desk at that ending.
+viralinfecticide How many times did you flip it? That's what we want to know!
+EHaraka 0.5 times, since it was "almost" flipped.
you really made a Parker Square™ out of that 3 indistinguishable dice cube
+Alex Banks Parker Cube™*
Best video I've seen. Completely absorbing! So cool how so many people get involved! Love your videos. Gutted the signed dice ran out already. (Thanks for the signed card though 😊). Trying to pluck up the courage to go to a maths club night - not quite up to speed yet though.
Keep the videos coming - they're great. Thank you 😄
Hey Matt!
Just wanted to say that I really enjoy and appreciate your videos!
Greetings from Finland. Thanks!
Did it take you 2,835 tries? (Video is 28:35)
or maybe an average of 28.36 times LOL
+DiCasaFilm That would be cool!
+DiCasaFilm That would be very clever of him. I have to admit I literally yelled "Matt no!!!" when he didn't give the answer at the end though....
Imagined if he never showed his face again. The mystery of the coin flips, forever shrouded in... more... mystery, yeah.
Oh my god the trickery with the hexagon my brain hurts
that has got to be the.best ending to a TH-cam video I have ever seen. seriously. many props!
Matt, I fear that you did not actually count the number of flips it took. Please give me closure.
THAT ENDING?! DON'T DO THIS TO ME, I'VE WAITED SO LONG! :'(
edit: Such a Parker Ending
+Fettklomp A Parker Square of an ending*
+888SpinR Well done, good sir!
+Fettklomp Parker square of a comment I might add ;P
Very parker square
"I've arranged them in a 10x10 grid... Of course missing the 3 in the corner..."
Looks like you arranged them into a bit of a Parker Square then ;)
Jokes aside, loving the videos, and while I couldn't really take part in this puzzle thanks to exams, I really enjoyed hearing the solutions people came up with and I'm looking forward to wracking my brain over the next one!
Winner well awarded, the solution was very true to the spirit of the challenge.
First off, thanks for taking such a great puzzle and bringing it to this community where we could all share our findings, intuitions, etc.. Also, I think you did an excellent analysis of a variety of solutions to this problem!
I will however assert that we have missed out that you have not done an analysis of the 3 to 2 dice solution I posted, as I it contains what appears to be a very powerful mathematical generalization! I stress this, not because "its mine" (I do not even attempt to take ownership! It is for any and all.), but because its really cool, and very few have approached it so far, presumably because it looks intimidating due to a perhaps a lack of emphasis of elementary algebra in modern mathematics.
Thank you for bringing this problem to such a large forum! I am very happy that I got the opportunity to participate socially about what would typically be a personal musing the results of which would be buried in a pile of notebooks.
All the best! :-)
+myName Thanks! I'm very proud of the community here. Sorry I didn't get to include your solution. There were so many good ones, I had to cut it down a bit arbitrarily.
I cant imagine trying to wade through all this! This has been awsome though! Thank you! :-D
28:36 FFFFFFFFFFFFFFFFFFUUUUUUUUU
that's my reaction exactly xD
+Nusm4 mine was "bastard" with a smile.
+Nusm4 I would say some rough word after that precise moment, but I won't. We deserve that after the efforts he puts into lookiing into all of our solutions xD
i love the Parker cube reference XD
+ST-Leo-TS GodGoneRogue It was awesome and unexpected!
For anyone who doesn't know what it is about, chekc Numberphile's channel, video: "The Parker Square"
If this was to be made as a marketable dice, you could have a semi transparent hexagon on all of the faces
Hows this for a solution:
Write the numbers 1 through 6 on the outside (clear) die, then take the mod(6) of the sum of inner dice
+elvishfiend Genius!
+elvishfiend I guess this would be an outside the box (like writing the numbers on the cube and rolling twice) solution which was excluded
Elchi King Literally! (As the ink from the marker you used would be on the outside of the box.)
+elvishfiend This method was mentioned in the orignal video and is not a valid solution. This is a maths problem, not a party trick.
+Tumbolisu Maths is srs bzns.
rly srs bzns.
You really Parker Squared that Parker Cube...
+vipero07 savage
I see that Matt Parker has come to terms with the Parker Square ( 22:22)
Nice touch showing the box assembly.
That cheeky solution of gluing one of the dice in place was really the most elegant one. Never saw it coming!
Lmao, the end...
+Patrick Wienhöft the first part of the word could be heard out as thr-
So I'm guessing it's in the 300's
Although for probability's spite, it could have been the 30's
+Jack Lam I'm thinking 3000s
+Jack Lam
if there is the [thr-] sound then we can rule out 30's due to its sound being [thur-]
i heard nothing.. but it looks like that's fricative which means the most significant digit must be 2, 3, 4, 5, 6, or 7 or it could begin with the number 10,or 12.
i still say three-ish
***** Looks like he's putting his tongue between his teeth, so it's almost definitely th-. I can't rule out the "thur-" sound.
God, the end was awesome!
I didn't know, that you really flipped that coin so often!
I'm in love with the *Parker cube*
that was a kewl video. man the graphics in this show constantly surprise me.
My favorite thing about these solutions is that it's way easier to just roll two dice.
The easiest solution is to just pick the number 1 twice. (Sure, it's the least random, but it's definitely easiest.)
@@johnnye87 Meh, you should choose 4 and 2. :p
Cliff hangers... gotta hate them...
Dang, I was looking forward to hearing your favourite solution.
Great job on solving the shipping problem, too.
That's one Parker Square of a first place trophy.
Parker cube!
loved this video and the previous one. Also, hilarious assembly required! I LOL'd. Woulda glued one in the corner myself!
You could have just taken those 97 dice, turned 16 to each face (1-6), and then used those 16 to form a surface to create a large signing of your name. You would only have to sign your name six times, each person would know which dice was which based off the portion of your signature, and the side the portion was on, and the last die could have been tacked on at any point to extend a rather dapper tail to the end of one of the signatures.
Even though this video is now over 4 years old, I decided to give it a go and try finding my own solution anyway. I spent a good couple hours working on it and I thought I found a novel solution, only to realize that my solution required distinguishing between the *indistinguishable* dice :'(
Here I am 7 months after you stumbling on this video. I learnt from the "simulate 1 die" warm up that trying to distinguish it is definitely not the correct path, but I am wondering, how many simply suggested to just "roll and mod 6, twice!" as a solution.
I mean, if they were distinguishable you could just ignore the same one every time lol.
You never actually did get 10 heads and 10 tails in a row did you
+Kram1032 He's probably still doing it. :)
Well, that's not what he was trying to do.
Loved that revelation at the end.
"What you need is to be CLEVER!"
Thank you, Matt, now we know.
I liked the gluing solution the best. ;)
You need to know the individual values for Monopoly. If they're both the same you get another go, get out of jail free, etc.
Two indistinguishable dice will do, you don't need to know which one is first and which one second.
No idea how I got to this video, but I really enjoyed it.
I appreciate your dedication to the viewers.
Parker cube.... I love it! Haha
the solution with the hexagon is really good. It is the only one I have seen so far, that is as fast as a lookup table and can be used while playing with children. (Or, if you do NOT have children (like me): while being a little drunk.)
+Ceragon little children == little drunk: TRUE
+standupmaths Lol.
22:19 Nice reference. I would've totally commented calling it a parker square of a trophy but this is much better.
The parker cube comment made me chuckle. Best line in the video.
lol!
first a square that does not work and now a damaged cube.
i am waiting for you to name a spoiled hyper cube.
Don't forget the Parker line and Parker dot for 1 and 0 dimensional objects!
Almost missed that one!
Matt accidentally made a paradox while saying : "... for going to far which is exactly the right distance to go ..." If to far is right then it is not to far so it is not right
***** I just really like paradoxes
yay! Paradox
It is not a paradox, it is simply a quantum superposition of states
A contradiction isn't a paradox. Besides, statements in this format generally mean that what an individual might think is going too far is, in reality, going just far enough.
Beat Button I know what he meant I just like finding paradoxes and what is a paradox if it ins't a self contradiction ?
Very clever solutions!
ok, i already knew you from numberphile but i just discoverd your chanel.
you own your sub ;), thank you to make me search and think about math problems
that ending tho. you cheeky *******
Honestly, Matt, you may well be the modern-day Martin Gardner, posing these puzzles to us like this.
+doctorwhofan883 More like ferma XD
I love the first 28 minutes and 35 seconds of your video.
There were some really nice solutions submitted.
WORST CLIFFHANGER EVER
I know right
Damn you matt.... are you going to make us watch annother 28 min video to know the coin flip number????
+Jarvis Anderson The flip video will hopefully be shorter.
I also "hope" :) Keep up the good work - you are a maths inspiration to my kids (and me).
21:36, I stood up and cheered!
Neat little side thing I discovered while playing around with this stuff: if you take two dice and say 1, 2, and 3 are 0, and 4, 5, and 6 are 6 on one die, and then keep the other die as is, you get an even distribution for the numbers 1-12 (like dolling a D12). I haven't figured out how to generalize it for other multiples of 6 yet.
Did you sign the Parker Cube as "Matt Paper"?
He really pulled a Parker Square there, didn't he?
+Noel Goetowski Maybe he means the paper he used; matt paper.
Actually you almost get the easiest solution to the 2 dice from 3 question.... Just glue one into a corner xD xD
lolllll
I investigated why the triangle numbers stop in the first puzzle, and it really is pretty interesting.
Rolling two dice can be represented by a 2-dimensional table, with the first die's result on one axis, the second die on the other, and the grid being the sum. You'll notice if you do this that it creates diagonal lines of the same number.
Similarly, you can step it up to three dimensions for three dice. This gives a cube of results. Also similarly, it creates diagonal planes of the same result. With a little imagination you can see that the first few planes are going to have triangle numbered size. However, the diagonal cross section of a cube does not stay triangular! Past 8 the cross sections become irregular hexagons. The tips of the triangles are being chopped off, so to speak. That's why the pattern doesn't hold all the way through.
First Parker Square, now Parker Cube... you're slowly becoming famous.