# Questions tagged [dice]

For puzzles involving rolling numbered dice.

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### 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 ...
1k 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 ...
337 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 ...
391 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 ...
667 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 ...
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 ...
171 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 ...
271 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, ...
1k 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 ...
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 ...
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 $6$ ...
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:" ...
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 ...
194 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 ...
4k views

1k 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 ...
222 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 &...
8k 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 ...