Problem:
For each real number x, let ⌊x⌋ denote the greatest integer that does not exceed x. For how many positive integers n is it true that n<1000 and that ⌊log2n⌋ is a positive even integer?
Solution:
Because
⌊log2n⌋=k⟺2k≤n<2k+1
in order for the integer k to be positive and even,