Q: Between 1000 and 2000 you can get each integer as the sum of nonnegative consecutive integers. For example,
147+148+149+150+151+152+153 = 1050
There is only one number that you cannot get.
What is this number?
A: 1024
You cannot get 1024 because it is a power of 2
it is 2 to the 10th power
It is the only power of 2 between 1000 and 2000
For example 15 = 1+2+3+4+5
14 = 2+3+4+5
17 = 8 + 9
but 16 cannot be the sum of consecutive integers
neither can 2, 4, 8, 32, 64, 128, 256, 512, 1024, 2048 etc
1 comment:
This is cool. I had not realized that a value which is a power of 2 had this property.
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