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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 $6$?

 Mar 30, 2020
 #1
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Product won't equal 6:  1 & 2;  1 & 3;  1 & 4; 1 & 5;  2 & 4;  2 & 5;  2 & 6;  3 & 4;  3 & 5;  3 & 6;  4 & 5;  4 & 6;  5 & 6

 

Product will equal 6:  1 & 6;  2 & 3

 

Just remember that you need not count duplicates; once you have counted  1 & 3  you don't count  3 & 1.

 Mar 30, 2020

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