# Difference between revisions of "Blank dice"

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When you roll two six-sided fair dice, the total number of dots displayed can be anything from 2 to 12. However, some sums are more likely than others. Now suppose you have two six-sided fair dice, with no dots on any of the faces (they are blank). Armed with only a marker pen and your puzzle-solving prowess, how can you draw dots on the dice so that each possible sum will appear with equal probability? | When you roll two six-sided fair dice, the total number of dots displayed can be anything from 2 to 12. However, some sums are more likely than others. Now suppose you have two six-sided fair dice, with no dots on any of the faces (they are blank). Armed with only a marker pen and your puzzle-solving prowess, how can you draw dots on the dice so that each possible sum will appear with equal probability? | ||

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+ | {{Hint | Some solutions are trivial, for example you could just leave all the sides blank so that the only possible sum (zero) appears with 100% probability. But thinking about the trivial solutions may well be the first step to finding better solutions in which each dice has a different number on each side.}} | ||

[[Category: Probability]] | [[Category: Probability]] |

## Revision as of 07:51, 22 October 2010

Here is a probability brain teaser that I remember from a math for elementary ed class I tutored.

## Puzzle

When you roll two six-sided fair dice, the total number of dots displayed can be anything from 2 to 12. However, some sums are more likely than others. Now suppose you have two six-sided fair dice, with no dots on any of the faces (they are blank). Armed with only a marker pen and your puzzle-solving prowess, how can you draw dots on the dice so that each possible sum will appear with equal probability?

**Hint**

Some solutions are trivial, for example you could just leave all the sides blank so that the only possible sum (zero) appears with 100% probability. But thinking about the trivial solutions may well be the first step to finding better solutions in which each dice has a different number on each side.