## Palindrome Squares

A palindrome is any number that reads the same forwards as backwards. Let \(P(N)\) denote the number of \(N\)-digit palindromes that are perfect squares.

Part A | Determine \(P(13)\) | |
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Part B | Determine \(P(25)\) |

## Consecutive Sums

Let \(f(N)\) denote the number of ways to express \(N\)
as a sum of two or more consecutive positive integers.
For example \(f(15)=3\) because \(15\) can be expressed as a
sum of consecutive positive integer in \(3\) different ways:

\(15 = 7+8 = 4+5+6 = 1+2+3+4+5\)

Part A | Determine \(f(25200)\). | |
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Part B | Determine \(f(100!)\). |