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Let S = {1, 2, 3, ..., 12}. How many subsets of S, excluding the empty set, have an even sum but not an even product?

 Jun 17, 2020
 #1
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thanks for the help!

 Jun 17, 2020
 #2
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I am really confused about this one, I thought the answer was 15 but that is wrong

 Jun 17, 2020
 #3
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So

 

even * odd = even

odd*odd = odd

even*even.= even

 

even+odd = odd

even+even = even

odd + odd = even

 

So for subsets containing 2 we must have 2 odds.Thus all odds work.

 

6odds-

 

 

6c2 = 15

 

 

 

Trios: We must have all odds, but odd+odd+ odd = odd.so thus there are no possibilities for subsets with odd amounts.

 

quadruplets:

Again, odd oddd odd odd

 

6c4, again we have 15

 

6-lets

 

1 choice, 6c6

 

Thus 15+15+1 = 31

 

Not sure if correct, but I think it its.

 Jun 17, 2020
 #4
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First off, the awnswer is NOT 31(I did it). And this person is a current participant in the MBMT Online Math Tournament. It is against the rules to use the internet to find solutions.

 Jun 17, 2020
 #5
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Ok I apologize for my error and for helping someone cheat

hugomimihu  Jun 17, 2020

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