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An ordinary 6-sided die has a number on each face from 1 to 6 (each number appears on one face). How many ways can I paint two faces of a die blue, so that the product of the numbers on the painted faces isn't equal to 6?

 Apr 21, 2020
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An ordinary 6-sided die has a number on each face from 1 to 6 (each number appears on one face). How many ways can I paint two faces of a die blue, so that the product of the numbers on the painted faces isn't equal to 6?     

 

   1 6     2 6     3 6     4 6     5 6        Looks like there are 13 ways.     

   1 5     2 5     3 6     4 5     

   1 4     2 4     3 4     

   1 3     2 3     

   1 2     

   .     

 Jun 27, 2026

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