MathDB

7. Peggy picks three positive integers between

1

and

25

, inclusive, and tells us the following information about those numbers:
[*] Exactly one of them is a multiple of

2

; [*] Exactly one of them is a multiple of

3

; [*] Exactly one of them is a multiple of

5

; [*] Exactly one of them is a multiple of

7

; [*] Exactly one of them is a multiple of

11

.
What is the maximum possible sum of the integers that Peggy picked?
8. What is the largest positive integer

k

such that

2^k

divides

2^{4^8}+8^{2^4}+4^{8^2}

?
9. Find the smallest integer

n

such that

n

is the sum of

7

consecutive positive integers and the sum of

12

consecutive positive integers.

Problem Statement