BrainDen.com - Brain Teasers
• 0

# transitive dice

## Question

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?

## 2 answers to this question

• 0

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.

##### Share on other sites
• 0

nicely done rain man - A+

## Create an account

Register a new account