# Tag Info

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 ...
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### Aproximating 100 by 6

As xnor points out in his answer, this question is basically asking for the way to most evenly distribute $6^n$ results among $100$ bins, and gives a very brief description of the solution. I'll go ...
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### How many tries to roll a 6?

The answer is indeed...             ...because the question is equivalent to...   Calculations:

### 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 ...
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### How to simulate one die with three dice?

I believe this set of dice satisfies all your requirements:

### Aproximating 100 by 6

Get 10 different d6 dices and describe them on paper. Next to each description, associate a unique number from 0 to 9. Put all those dices in an opaque bag (you should have one to transport that near-...
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### Loaded Dice with Uniform Sum

To explain, here is a more formal way to state Ian's answer: Let the probability of die A rolling $i$ be $a_i$ for $1\le i\le6$, and similarly for die B. If every sum has the same probability, then ...
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### A Short Dice Puzzle

The answer is Proof Alternative proof
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### A new six-sided die

As already mentioned, the smallest possible sum is 27, resulting from the numbers 1, 2, 4, 5, 7, 8 arranged like this: 1 4758 2 Optimality is a consequence of ...

### 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 ...
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### 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 +...

### Aproximating 100 by 6

Figured i'd add my comment as an answer: We roll 3 dice $(D1,D2,D3)$, which we seperate spatially or in some other way (we used to use 3 different colors). We reroll D1 and D2 if they land on 6, and ...
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### 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 ...

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### A dice game, what is the optimal strategy?

Strategy: Expectated gain: Conclusion:

### 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 (...

### Aproximating 100 by 6

As @MikeEarnest says, unless you put an upper limit on the number of rolls, you can always do better with more rolls. Since $6^n$ is never divisible by $100$, you can never be completely fair. With ...
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### The Sphinx's Dice

The post linked in rand al'thor answer optimized the worst case pick the visitor of the sphinx can make. But the question asked for the best average case. A better solution in that case is: ...

### 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 ...

### 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: ...
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Easy:
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### 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, ...

### A new six-sided die

Can I use a barrel die? Then we could do an arrangement of for a sum of We can also do which works even better, since opposing faces have the same sum.
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### Two Dice = Nine Cards

The cards are numbered: Reasoning: There are 36 possible ways to choose two cards out of nine, so the results must be $2,3,3,4,4,4,\ldots,11,11,12$. If we sum all of these, we find that the total is ...