Every positive integer can be expressed in a unique way as the sum of powers of 2. Express 2008 as the sum of powers of 2.

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- Nov 3rd 2008, 06:32 PMnancymcwilliamspowers of 2
Every positive integer can be expressed in a unique way as the sum of powers of 2. Express 2008 as the sum of powers of 2.

- Nov 3rd 2008, 10:33 PMajj86Possible solution
I don't know if this is what you were looking for, but I got an answer:

42^2 + 12^2 + 10^2 = 2008

I started by squaring 45 and then moving back from there with 44, 43 and so on. I then subtracted this squared value from 2008. When I got to 42^2, which equals 1764, I subtracted it from 2008 and got 244.

244 = 144 + 100

244 = 12^2 + 10^2

I then added these two squares to 42^2 and got 2008. - Nov 3rd 2008, 10:53 PMearboth