Skip to main content
54 votes
Accepted

Deceptive dice game

You can make arbitrarily large sets of dice with this property. Start with Efron's dice: A: 4, 4, 4, 4, 0, 0 B: 3, 3, 3, 3, 3, 3 C: 6, 6, 2, 2, 2, 2 D: 5, 5, 5, 1, 1, 1 A beats B, B beats C, C ...
f'''s user avatar
  • 33.7k
43 votes
Accepted

How many tries to roll a 6?

The answer is indeed...             ...because the question is equivalent to...   Calculations:
humn's user avatar
  • 21.9k
40 votes

How many tries to roll a 6?

This surprisingly beguiling puzzle may also be solved with a surprisingly unsophisticated approach. Symmetry, by itself, predicts the average length of evens-only sequences ending with 6 to ...
humn's user avatar
  • 21.9k
33 votes
Accepted

How to simulate one die with three dice?

I believe this set of dice satisfies all your requirements:
Deusovi's user avatar
  • 147k
25 votes
Accepted

A Short Dice Puzzle

The answer is Proof Alternative proof
hexomino's user avatar
  • 137k
23 votes

How to simulate one die with three dice?

@Deusovi's answer is totally correct, but I want to add here the general approach for solving such problems as well. No need to upvote, since I did not invent the technique, and you can see it ...
Puzzle Prime's user avatar
  • 6,964
23 votes
Accepted

A Short Dice Puzzle II

Answer: Explanation:
AHKieran's user avatar
  • 7,282
22 votes
Accepted

Make 2 dice out of 3 dice

All addition is modulo 6 (e.g. 4 + 3 = 1, 3 + 3 = 6, 5 + 3 = 2, 6 + 1 = 1). 3 Dice Roll Resulting 2 Dice Roll Two same, one different: AAB AB 135 14 246 25 All same: AAA 36 Three in a row: A, A +...
Mike Earnest's user avatar
  • 32.5k
20 votes
Accepted

8 dice with a product being a square

The only prime factors of the numbers 1 through 6 are 2, 3, and 5. Therefore the factorization of the numbers on the paper will only consist of these primes, i.e. they will be of the form: $$ 2^a 3^b ...
2012rcampion's user avatar
  • 18.9k
19 votes

A Boyfriend's Mysterious Message

monoRed's user avatar
  • 474
19 votes
Accepted

A dice game, what is the optimal strategy?

Strategy: Expectated gain: Conclusion:
w l's user avatar
  • 4,992
19 votes

Fair d5 with as few faces as possible

Surely will suffice for all n > 2. Consider a symmetrical cone with an n-sided regular polygon as its base. If we take a "stubby" one (of a shortish height) and a "pointy" one (...
Bass's user avatar
  • 77.7k
16 votes
Accepted

Date Dice Dilemma

My answer: Numbers on each die: Reasoning: . Additional reasoning:
Marius's user avatar
  • 18.2k
15 votes

How many tries to roll a 6?

Let $X_n$ be the event that the dice takes $n$ rolls to get the first 6, given all the rolls are even. Let $A_n$ be the event that it takes $n$ rolls to get the first 6, and let $B$ be the event that ...
boboquack's user avatar
  • 22k
14 votes

Three Dice minimum value

The answer is First I show that a lower number is not possible: This establishes a lower bound. The upper bound is established by providing an actual solution. First die: Second die: Third die: ...
kasperd's user avatar
  • 1,287
14 votes
Accepted

A Pair of Odd (but Still Balanced) Dice

Easy:
JMP's user avatar
  • 35.6k
14 votes
Accepted

Chain Puzzle: Tabletop Games #05 - It's Yahtzee, Jim, but not as we know it

I rotated the grid 90 degrees clockwise before solving the grid deductions, in order to reduce vertical space. Let's solve Statue Park first. Now to the Fillomino. Now that the two grids are solved, ...
Bubbler's user avatar
  • 15.5k
12 votes
Accepted

Putting the pips on a d6

I make it
UselessInfoMine's user avatar
12 votes
Accepted

Two dice with the same probability for each sum?

I think: Here's my proof:
JS1's user avatar
  • 17.9k
10 votes

Three Dice minimum value

A lower bound is An upper bound is
Shagnik's user avatar
  • 496
10 votes
Accepted

Generating Roman numerals with dice

UPDATE (after a pretty sturdy hint from OP): (Again, one more number can be constructed, if flipping the dice is allowed.) Original answer: I got all the way up to with these dice: Here's how to ...
Bass's user avatar
  • 77.7k
10 votes
Accepted

A bet with your friend

Suppose we have $n$ dice. Then When $n=15$ Just for fun, here's a smartass combinatorial way to prove the identity I used above: Perhaps there's a smarter-ass way to do it a bit more briefly.
Gareth McCaughan's user avatar
9 votes
Accepted

Building the ideal Scrabble dice set

I chose to use a standard set of D&D dice, as you might get from a game shop, for ease of manufacturing and rolling. Incidentally, it contains seven dice, which is the number of tiles that form a ...
Sconibulus's user avatar
  • 19.7k
9 votes

How many tries to roll a 6?

I believe the answer is This is computational calculation, so it is not statistical answer. It is for the people who try to find it probabilistically. Here is the probabilistic solution: First of ...
Oray's user avatar
  • 30.4k
9 votes

Putting the pips on a d6

I decided to solve this in the second hardest possible way myself, and created a 3D model of all the possibilities. Here it is: The sides that are not visible are fully determined by the visible ones,...
Bass's user avatar
  • 77.7k
8 votes

What is the 'best' way to tilt through a D20?

One should note that we may break this problem down into a number of subproblems: What is the path from $n$ to $n+1$ containing the least number of negative points? It is relatively clear that ...
Milo Brandt's user avatar
  • 7,891
8 votes
Accepted

Cheating aplenty at Build-a-Die 2017

I wrote up some Python code to find the optimal solution in each case. Here are the dice everyone chose: And here's who won:
praosylen's user avatar
  • 993
8 votes
Accepted

A strange message full of dice came in my mail

It seems to translate to: Found by
Fifth_H0r5eman's user avatar
8 votes
Accepted

Fair d5 with as few faces as possible

By "symmetric", I mean that there should exist symmetries of the polyhedron mapping each of the five stable faces to each other. Sets of independent symmetry elements The symmetry of a ...
John Bollinger's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible