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To express 20 as a sum of different powers of 2, we would write 20 = 2^4 + 2^2. The sum of the exponents of these powers is 4 + 2 = 6. If 600 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers?

 Dec 26, 2020
 #1
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29.226412193 = 599        20 = 1         9.226412193 + 0 = 9.226412193

 Dec 26, 2020
 #2
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I was assuming integer exponents

 

I get 

 

2^9 + 2^6  + 2^4  + 2^3  =

 

512  + 64  + 16 +  8  =

 

576  + 24   =

 

600

 

So.....exponent sum  =   9 + 6 + 4 + 3   =  23

 

Anyone else  ???

 

cool cool cool

 Dec 26, 2020

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