I need math help!?

Question

1) The largest integer that is not a sum of distinct powers.
2)The only perfect number of the form x to the nth + y to the nth
3)The number of days in a lunar cycle.
4) The cube root of this number is one more than the smallest prime.
5) The factor of every palindrome with an even number of digits.
6) The first of two consecutive numbers whose factors have the same sum.
7) The lease number of moves in the Tower of Hanoi puzzle with 5 disks
8) One of the two numbers that can be both the perimeter and the area of the same rectangle
9) A number n where if the sum of the digits of the number is divisible by n, then the number itself is divisible by n
10) One of the four number where n! has n digits
11) The only number whose spelling contains the same number of letters as the number itself.
Please help with any or all you may know!

Answer 1

1) 23 (see reference below)
2) 28 = 1³ + 3³. (I think this one needs to specify that n > 1, because, for instance, 6 = 4¹ + 2¹.)
3) 29.53 (see reference below)
4) smallest prime is 2, 2 + 1 = 3, 3^3 = 27
5) 11
6) 14 (1 + 2 + 7 + 14 = 24, 1 + 3 + 5 + 15 = 24)
7) 2^5 - 1 = 31 (see reference below)
8) x² = 4x, x² - 4x = 0, x = 4...so the area/perimeter is 16.
9) works for either 3 or 9
10) 22! = 1,124,000,727,777,607,680,000. (or 1...)
11) four

Answer 2

1) 23 (see reference below)
2) 28 = 1³ + 3³. (I think this one needs to specify that n > 1, because, for instance, 6 = 4¹ + 2¹.)
3) 29.53 (see reference below)
4) smallest prime is 2, 2 + 1 = 3, 3^3 = 27
5) 11
6) 14 (1 + 2 + 7 + 14 = 24, 1 + 3 + 5 + 15 = 24)
7) 2^5 - 1 = 31 (see reference below)
8) x² = 4x, x² - 4x = 0, x = 4...so the area/perimeter is 16.
9)3 or 9
10) 22!
11) four

Answer 3

3) 28
4) x^1/3 = 2 + 1 (2 is the smallest prime)
x^1/3 = 3
x = 27
6) 14 (1, 2, 7, 14) and 15 (1, 3, 5, 15)
8) x²-4x = 0...x = 4
11) four

Answer 4

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Answer 5

...
4) 27
5) 11 (maybe?)
...
8) 16 (4x4 square, which is a rectangle)
9) 9. This is the test for a number being divisible by 9.
10) 1. 1! = 1
11) four (4)

Answer 6

4. I think the answer is 8
11. Four

Answer 7

All I can say is... Good luck! Those are the very questions that put an end to my College days.

Take it easy!

joe

Answer 8

3 is twenty nine
4 is twenty-seven
8 is four
11 is four

Answer 9

OMG hey! Pst It's me. Jenn... HAHA . yeah hey. i hate math. just saying.

Answer 10

OMG! What the hell kinda math are you taking?