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# transitive dice

## 3 posts in this topic

Posted · Report post

it's possible to construct a set of 3 dice, such that no matter what dice your opponent picks first, the dice you pick will beat it.

```
1v2 1 4 4 4 4 4

2 2 1 1 1 1 1

2 2 1 1 1 1 1

2 2 1 1 1 1 1

5 2 2 2 2 2 2

5 2 2 2 2 2 2

5 2 2 2 2 2 2

2v3 3 3 3 3 3 6

1 3 3 3 3 3 3

4 2 2 2 2 2 3

4 2 2 2 2 2 3

4 2 2 2 2 2 3

4 2 2 2 2 2 3

4 2 2 2 2 2 3

3v1 2 2 2 5 5 5

3 3 3 3 1 1 1

3 3 3 3 1 1 1

3 3 3 3 1 1 1

3 3 3 3 1 1 1

3 3 3 3 1 1 1

6 3 3 3 3 3 3

```

is it possible to construct a set of 5 dice such that the total of any two dice can be beaten by the total of two other dice?

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Posted · Report post

Yes! Doing the math was hard work though.

Die 1: 1 1 4 5 5 5

Die 2: 1 4 4 4 4 4

Die 3: 2 2 2 5 5 5

Die 4: 3 3 3 3 3 6

Die 5: 3 3 3 4 4 4

1,2 is beaten by 4,5.

1,3 is beaten by 2,4.

1,4 is beaten by 2,3.

1,5 is beaten by 2,3.

2,3 is beaten by 4,5.

2,4 is beaten by 1,5.

2,5 is beaten by 3,4.

3,4 is beaten by 1,5.

3,5 is beaten by 1,2.

4,5 is beaten by 1,3.

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Posted · Report post

nicely done rain man - A+

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