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No calc please.

 May 28, 2019
 #1
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The number 12 can be broken up to \(x^2*y^2\), since the number of factors is \((2+1)(2+1)=3\cdot3=9.\) The three numbers do not work here since there are no possible outcomes.

 

Thus, we can have: \(2^2*3^2=36.\)

 

\(2^2*5^2=100.\)

 

\(2^2*7^2=196.\)

 

I do not think any more possible outcomes are there, and you can still check my work.

 

Thus, the answer is \(36+100+196=\boxed{332}.\)

.
 May 28, 2019

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