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There are 31 perfect square numbers between 1 and 1000 (including 1).
The two perfect numbers between 1 and 30 are: 6, 28
A near-perfect number is one that is close to being a perfect one (obvi). So to find out if it's perfect or not (there are other terms, but that doesn't really matter right now), you add up it's divisors other than itself. So for example: 6 is a perfect number because 1+2+3+6. 16 1+2+4+8=15, so thus it is near-perfect. The four perfect numbers are 6, 28, 496, 8128
500.5 Because: 1+2+3+.......998+999+1000 Add 1 to 1000 equaling 1001. This makes a pair. There are 500 more of these so 500 pairs. So 1001x500= 500500 Finally divide it by 1000 because there are 1000 numbers. (1000-1=999+1=1000) Concluding the answer to be 500.5 :)
There are 107 numerical palindromes between the numbers 1 and 1000, starting from 2 to 999.