Monday, March 12, 2007

Sums, Squares and Somethings

Partition {1,2,..,16} into 2 sets such that the sum of the numbers in one set equals that in the other, and likewise for sum of squares and sum of cubes.


Anonymous Anonymous said...

should do it.

8:55 AM  
Anonymous Anonymous said...

For Squares A={16,15,13,9,4,1} B={2,3,5,6,7,8,10,11,12,14}

Left the cubes case for the third person.

-- second person

12:51 PM  
Anonymous Anonymous said...

First Poster:

Brilliant solution. I misunderstood the problem statement.

-- Second poster/person

1:24 PM  
Blogger metoo said...

Consider the set {1,....,n} and partition it into 2 sets so that the sum of i-powers of the numbers in the two sets are the same, for i=0,1,2, ....

9:42 PM  
Anonymous Anonymous said...

metoo, my guess is that you can only consider the first ~log(n)-1 moments; in which case it does not seem to be hard to find a solution (simple generalization of the case n = 2^k: the solution will be inductively constructed - express n as 2^k(2q-1) for the generic even case). Do you have a prove of uniqueness - even for the perfect power of 2 case?

2:37 PM  
Anonymous Anonymous said...

sorry, I meant "Do you have a prove of uniqueness for the perfect power of 2 case?" Thanks :)

2:39 PM  

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