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Questions tagged [dice]

For puzzles involving any form of dice.

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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 ...
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 ...
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 ...
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 ...
3 votes
0 answers
221 views

Perfect 9-sided die [closed]

I am working on a fair 9-sided die and I settled on a design where you select three edges of a cube where the two sides that one edge touches don't overlap with any of the other sides touched by the ...
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 ...
3 votes
1 answer
147 views

Two pairs of dice with the same probability [duplicate]

Alice has two dice each numbered from 1 to 6. Bob has two dice as well, the numbering is not known, but each face has a positive integer. The numbering on each dice can be different and a number can ...
3 votes
1 answer
222 views

What is the most STAMINA-efficient strategy to escape the well?

You are roleplaying as an adventurer under the direction of a sadistic DM who has just thrown your character down a well. In order to escape, you have unlimited chances at a STAMINA check, difficulty ...
0 votes
1 answer
944 views

What is the pattern here? Rolls of five dice correspond to numbers [duplicate]

What is the pattern in this puzzle?
-2 votes
2 answers
3k views

Petals around the rose

You roll 5 dice and I'll always be able to give a number uniquely-defined by the numbers on the dice. You have to figure out how it works, without looking it up. Here's a couple example rolls: 1,2,3,4,...
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:" ...
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 ...
-4 votes
1 answer
643 views

Open dice Problem

The following figure is folded to form a box. Choose from the alternatives (A), (B), (C) and (D) the boxes that is similar to the box formed. Source: YouTube Video How to answer these type of ...
1 vote
2 answers
185 views

Why box (3) isn't possible and why box (4) is possible? [closed]

The figure given on the left hand side is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed. Source: IndiaBix I understood that box (...
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. ...
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] ...
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 ...
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 ...
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 ...
-3 votes
1 answer
195 views

please help me with this logic based question.what is the missing block? [closed]

Please complete the figure with one of 9 blocks below.
3 votes
1 answer
125 views

Quarter Rolling Die

Quarter rolling a die means triping it on any of the 4 sides adjacent to its base or face in contact with the flat surface. Using the assembled die and quarter chessboard: You can place and align the ...
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 ...
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-...
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: ...
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 ...
2 votes
1 answer
260 views

Four unfair dice

On a table there are four standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each. Alice starts and chooses a die. Then Bob chooses a die and both throw the dice. The winner is the person ...
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 ...
3 votes
1 answer
418 views

Four dice puzzle: Postscriptum

This continues (and completes) the sequence of four dice puzzles: Four dice puzzle: 2,2,4,5 Four dice puzzle: What's the best throw? The days go by and Damiano is still throwing his four dice. He ...
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 ...
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 ...
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 ...
1 vote
2 answers
208 views

Is it easier to control an unfair die than a fair die? [closed]

First of all, I am not sure if this is the right place to ask this question, I wanted to post it at the mathematics community but also wasn't too sure. I read somewhere that when dice are fair, the ...
5 votes
1 answer
356 views

A strange message full of dice came in my mail

So I got a package today that contained the strangest contents. It was a set of dice, each of them numbered in one of the corners. Arranged, this is what numbers or characters displayed on each dice, ...
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 ...
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 ...
4 votes
4 answers
2k views

A Short Dice Puzzle II

A standard $6$-sided die is put inside a cup. The cup is shaken and put upside-down, hiding the die. You are going to guess what is the number on the top of the die. But, instead of given $6$ options, ...
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 ...
3 votes
4 answers
248 views

Randomly selecting cards using 6-sided dice

There is a pile of $5\leq N\leq15$ cards. $x=3$ or $6\leq N$ cards need to be randomly chosen from this pile (uniform distribution). To do this any number of $6$-sided dice can be rolled any number ...
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 $...
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 ...
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 ...
-4 votes
2 answers
141 views

New Dice Table at the Casino [closed]

You walk up to a dice table in the casino. A woman bets on $12$, throws the dice and they come up: 6 5 3 2 She shouts with glee as the dealer hands her the ...
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 ...
2 votes
1 answer
170 views

Dice problem involving nine randomly selected cups [closed]

I was given this problem by a colleague, and I cannot figure it out. Given nine cups and an unlimited supply of six-sided dice rolled one at a time, what is the probability that you will, at some ...
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 ...
2 votes
1 answer
289 views

Another Unconventional Dice Blackjack game - is Nash equilibrium here?

This question is similar to This Dice Blackjack game - is there Nash equilibrium?, but the game rules are completely different. This Dice Blackjack is game for two. It is also played with fair six-...
2 votes
3 answers
660 views

This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
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 ...
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 ...
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 ...