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Questions tagged [dice]

For puzzles involving any form of dice.

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50 votes
7 answers
11k views

How many tries to roll a 6?

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ...
43 votes
3 answers
4k views

Relabeling two 20-sided dice without changing their total

Usually, 20-sided dice are labeled with the numbers 1 to 20. When you roll two of these, their sum is a random number between 2 and 40. The total 21 is most likely to occur, while 2 and 40 are the ...
Mike Earnest's user avatar
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41 votes
22 answers
9k views

Aproximating 100 by 6

You're a fan of pen & paper RPGs and have finally arranged a new playing group, recruited amongst your friends from the mathematical faculty. As a GameMaster (GM) you've assumed that all your ...
BmyGuest's user avatar
  • 18.2k
37 votes
2 answers
4k views

A Boyfriend's Mysterious Message

Imogen was dog-tired, but excited! After 3 gruelling weeks of 16-hour work days imposed by an iron-willed boss, she was finally finished all her projects. She'd been processing (figurative) ...
GentlePurpleRain's user avatar
37 votes
6 answers
2k views

Magician, assistant, nine dice, and two cups

A magician and her assistant are performing a magic show today, and you are the only audience member. Since it is a Thursday, the magician is saving her strength for the inevitable dragon attack and ...
zeb's user avatar
  • 1,103
27 votes
10 answers
4k views

Make 2 dice out of 3 dice

This question was first posted by standupmaths on youtube: https://www.youtube.com/watch?v=xHh0ui5mi_E He already got some answers but I think this community can probably find a better answer. ...
Sumyrda - remember Monica's user avatar
23 votes
3 answers
2k views

Gambling in a rigged casino

A well-known crooked casino is offering the following bet with a pair of (identically looking and indistinguishable) dice that both show the numbers $1,2,3,4,5,6$ on their faces. The first die ...
Gamow's user avatar
  • 45.6k
22 votes
3 answers
3k views

Fair results with unfair die

You are given a 6-sided die.The die is biased, so it is more likely to produce some results than others, but you don't know the exact odds. It is however given that the odds are the same for each roll,...
aaaaaaaaaaaa's user avatar
  • 2,079
21 votes
5 answers
1k views

Three Dice minimum value

You shall form three dice, placing 18 distinct integers on the faces of three cubes. Your goal is to be able to obtain all the integers between 1 and 216, inclusive, as the sum of the integers on the ...
rasim's user avatar
  • 211
21 votes
8 answers
2k views

A Short Dice Puzzle

There are $2$ fair dice: An $11$-sided die, valued from $-5$ to $5$, A $41$-sided die, valued from $-20$ to $20$. You pick one, and I'll take the other one. We roll the dice, and whoever rolls the ...
athin's user avatar
  • 34.2k
18 votes
1 answer
787 views

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

This is the fifth Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or ...
Stiv's user avatar
  • 144k
18 votes
4 answers
743 views

How many rolls on average to get N dice to all show the same value?

So for example: if $N = 3$ I roll and get -> $1,2,3$ I re-roll the $2$ and $3$ -> $1,4,4$ I re-roll the $1$ -> $2,4,4$ I re-roll the $2$ -> $4,4,4$ In this case, it ...
GroovyDotCom's user avatar
17 votes
15 answers
6k views

How to get a uniform 1 out of 7 chance, using only a coin and a 6-sided die [closed]

There are seven days in a week. Let's say you want to pick one at random, such that each day has an equal chance of being picked as each other day. In other words, the goal is to obtain a uniform ...
DrZ214's user avatar
  • 297
17 votes
5 answers
1k views

Generating Roman numerals with dice

This puzzle is closely based on this one: Generating numbers with cubes Now we want to generate Roman numerals by placing up to three 6-sided dice side by side. We are allowed to write multiple ...
Dmitry Kamenetsky's user avatar
17 votes
2 answers
2k views

Rolling Dice puzzle

The answer is a six-letter word. Here's an attempt at a text version, but you're really better off looking at the picture. Rolling Dice To get a full tour, you must be a man of many faces and ...
xnor's user avatar
  • 27k
17 votes
1 answer
792 views

Two Dice = Nine Cards

I have nine cards, each labeled with a real number (possibly negative or fractional) in a special way. When I randomly pick two of these cards without replacement and add their labels together, the ...
Mike Earnest's user avatar
  • 32.4k
15 votes
7 answers
3k views

Loaded Dice with Uniform Sum

A loaded die looks like a regular six-sided die, but instead of each number 1-6 being equally likely, some numbers may be more or less likely than others. Is it possible to have two loaded dice so ...
Mike Earnest's user avatar
  • 32.4k
15 votes
3 answers
2k views

The Sphinx's Dice

"I'm bored of riddles, I'm going to ask you a question about dice instead", says the Sphinx. "Now, I've got this set of Efron Dice here. There's four dice, and they have these values on their faces:" ...
A E's user avatar
  • 8,802
15 votes
3 answers
2k views

Date Dice Dilemma

My cousin just learned about numbers and dates in school and I would like to give him a little present: A set of (regular, six-sided) dice with which he can display the current date if he turns them ...
Timme's user avatar
  • 546
15 votes
2 answers
1k views

Crazy Dice - Unusual Dice with Usual Sum

Can you design two six-sided dice (different from the standard ones), where each face has a nonzero number of dots, so that the probability distribution of their total is the same as for two standard ...
Mike Earnest's user avatar
  • 32.4k
14 votes
2 answers
6k views

How to simulate one die with three dice?

I do not know if there is a correct solution to this puzzle, but I can't stop thinking about it, so here goes: is it possible to accurately simulate a single, fair, six-sided die using three custom ...
TheSoundDefense's user avatar
14 votes
7 answers
6k views

Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon $...
Alexis's user avatar
  • 8,302
14 votes
5 answers
2k views

The Good, the Bad and the Ugly

Tuco, Blondie and Sentenza play a game with a single die. Tuco has the first roll, then Blondie, and then Sentenza, and so on. As soon as a player tosses a six, that player drops out of the game and ...
Alexis's user avatar
  • 8,302
14 votes
5 answers
2k views

Who's favored in this dice game?

Alyson and Bethany decide to play a game involving a (standard six-sided) die. Alyson goes first, and rolls the die: if she rolls a 6, then she wins. Otherwise, Bethany takes the die and rolls until ...
Steven Stadnicki's user avatar
14 votes
2 answers
957 views

Counting numbers with 3 dice

Yesterday I saw a pair of calendar dice that can be rotated and swapped to show all days of a month between 01 and 31. The dice have a digit painted on each face. First die: [0, 1, 2, 3, 4, 5] ...
GOTO 0's user avatar
  • 13.5k
13 votes
4 answers
3k views

A dice game, what is the optimal strategy?

Alice was walking on the street when she came across a man playing with a die. She could not help trying to check if the die was loaded and while she was concluding that it wasn't loaded, the man ...
Untitpoi's user avatar
  • 2,700
13 votes
1 answer
1k views

Diabolical dice!

I have two 6-sided dice which between them have 12 different numbers, but some of the numbers are hard to tell apart because one is the same as the other upside down (like $89$ and $68$). I throw the ...
Rand al'Thor's user avatar
12 votes
3 answers
3k views

A new six-sided die

Enrico wants to construct a new six-sided die with the following properties: Each side should show a positive integer Different sides should show different integers If two sides share an edge, then ...
Gamow's user avatar
  • 45.6k
11 votes
1 answer
3k views

Deceptive dice game

You must create a set of 6-sided dice and play a game with an opponent. The dice are like regular dice, but you can change the numbers on the dice. For example, regular dice have sides ...
ghosts_in_the_code's user avatar
11 votes
1 answer
862 views

8 dice with a product being a square

8 standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each are thrown at the same time and the product of the dice is written down on a paper. This process is repeated until you are able to ...
ThomasL's user avatar
  • 12.2k
10 votes
4 answers
843 views

Nerves of Steel (a dice game)

A carnival offers a game, called Nerves of Steel. It is played with a standard die, except that the "six" has been replaced with a skull. You start by paying $7, then rolling the die. Each time you ...
Mike Earnest's user avatar
  • 32.4k
10 votes
5 answers
573 views

Find the optimal strategy for this dice game

You are playing a game: You have $6$ standard 6-sided dice that are all rolled at the start of the game. The sum of dice values is your score. Each turn, you can take any (or none) dice and reroll ...
BoltKey's user avatar
  • 431
10 votes
1 answer
518 views

Recipe for diced shark fin

How may the following shark-fin-shaped Goal distribution be cooked up with 44 ingredients in a roll recipe R based on the roll sum of two 6-sided dice with non-standard allotments of dots? Goal: ...
humn's user avatar
  • 21.9k
10 votes
8 answers
1k views

A Lazy Way to Make Two Dice from Many

Recently, I stumbled upon the puzzle: Make Two Dice out of Three, which asks for a solution to a case of the following question: Suppose I roll $n$ indistinguishable dice. From purely the $n$ ...
Milo Brandt's user avatar
  • 7,881
9 votes
3 answers
2k views

Putting the pips on a d6

Using a blank cube and a bunch of circular stickers, an average person constructs a d6. A d6 is also known as a six-sided die, or sometimes, a dice. For the purpose of this puzzle, the average person ...
Bass's user avatar
  • 77.6k
9 votes
3 answers
1k views

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

A regular D20 die (icosahedron) as depicted above has the number 1 to 20 arranged on its faces such that the sum of opposing faces is 21. Each triangular face touches three other faces directly by a ...
BmyGuest's user avatar
  • 18.2k
9 votes
3 answers
2k views

A first choice die

You and your friend have met to play a game of dice. This is a very simple game where both players roll a die at the same time, and the player with the lower score pays a coin to the other player. In ...
GOTO 0's user avatar
  • 13.5k
9 votes
2 answers
570 views

Cheating aplenty at Build-a-Die 2017

Each year, 9 affluent acquaintances meet to compete in a unique game of chance: each creates a fair six-sided die and rolls against each opponent 100 times -- the player with the most total wins in ...
Roland's user avatar
  • 9,753
9 votes
1 answer
239 views

2 of 4 cards for 1 die

These are equivalent to using using a deck of 4 cards to emulate a 6-sided die. A. Assign integer values to   a, b, c, d   so that the 6 possible &...
humn's user avatar
  • 21.9k
9 votes
1 answer
462 views

Four dice puzzle: What's the best throw?

This continues Damiano's puzzle "Four dice puzzle: 2,2,4,5" Damiano keeps throwing his four dice. After a lot of throwing and thinking and working, he has determined for every throw $a,b,c,d$ of his ...
Gamow's user avatar
  • 45.6k
9 votes
0 answers
283 views

Rolling dice in a box

A box containing identical dice that were arranged to have same orientation has a missing die at the center (see figure). The dice moves to the free space for they can change orientation and ...
TSLF's user avatar
  • 6,656
8 votes
3 answers
1k views

Building the ideal Scrabble dice set

This is a genuine question and I don't know the "correct" answer to this. I'm also of two minds if it is really on-topic on the site. Finding the answer is surely "a puzzle" (if ...
BmyGuest's user avatar
  • 18.2k
8 votes
2 answers
742 views

Four dice puzzle: 2,2,4,5

Damiano has thrown four dice and the numbers 2, 2, 4, 5 showed up on top. Damiano asks himself: What is the smallest positive integer that cannot be generated with these four numbers according to ...
Gamow's user avatar
  • 45.6k
8 votes
1 answer
445 views

Stickered Dice Game

You and your friend play a game. To begin with, each of you has an unlabelled die. On the table laid in front of you are 12 stickers labelled 1-12. The first player chooses one of the stickers and ...
mintmocha's user avatar
  • 175
7 votes
4 answers
2k views

Fair d5 with as few faces as possible

Challenge: design a polyhedral die that will always give one of five outcomes, each with equal probability. While achieving that, minimize the total number of faces of the die. Think of the die as ...
isaacg's user avatar
  • 7,129
7 votes
1 answer
1k views

A Pair of Odd (but Still Balanced) Dice

I have a pair of odd six-sided dice at my house... I don't quite remember where I got them. Each die has only one number on each side, and each of these numbers is a positive number. Each pair of ...
Excited Raichu's user avatar
7 votes
2 answers
437 views

West face East face

The 1 x 1 x 2 die with new configuration was created from 2 dice (with opposite faces totalling 7) that were glued together on one of their faces. If this long die is rolled twice, the sum of non-...
TSLF's user avatar
  • 6,656
6 votes
4 answers
1k views

A bet with your friend

James, your friend, has invited you to bet with him. He has a fair die, with $3$ faces showing $0$ and $3$ faces showing $1$. You pay him $\\\$70$. He throws the die $15$ times, and records the sum of ...
Culver Kwan's user avatar
  • 5,792
6 votes
1 answer
434 views

An extremely fair die

I have in mind a special kind of die, one that is even more fair than uniform density dice. If the die has $n$ faces with labels going from $1$ through $n$, then some faces will be larger than others ...
AureySteader's user avatar
5 votes
6 answers
2k views

Two dice with the same probability for each sum? [duplicate]

A friend invites you to play a game. The game is using two standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each. As usual, the dice are considered distinguishable, i.e. throwing a 1 with ...
ThomasL's user avatar
  • 12.2k