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Daily Brain Teaser / Puzzle
April 06, 2007
Previous Days Teaser -- Want More? -- Next

The numbers on a die are not placed at random. On every pair of opposite faces the sum of the numbers is 7: 6 is op­posed to 1, 5 to 2, and 3 to 4. There are several other ways of placing six numbers on a die. How many ways are there altogether?

VIEW SOLUTION BELOW

THE SOLUTION

We can place the number 1 anywhere. Then there are five ways of choosing the number which will be opposite the 1. Imagine that the 1 and its opposite are on the top and bottom of the die. We still have to place the four remaining numbers on the four remaining faces around the die. Let X be one of these numbers. There are three ways of choosing its opposite number. Then there are two ways of placing the last two numbers. The total number of ways is: 5 x 3 x 2 = 30. None of these 30 dice can be turned into one of the others by rotating it in any direction.