Arrange numbers 1 to 17 in a row such that the sum of every adjacent pair is a perfect square.

Here are the solutions to the number arrangement puzzles:

Part 1: Arranging numbers 1 to 17 in a row

The goal is to arrange the numbers from 1 to 17 (without repetition) in a row such that the sum of every adjacent pair is a perfect square. The perfect squares to consider for sums of numbers between 1 and 17 are $4, 9, 16, 25$.

Step 1: List all possible pairs $(a, b)$ from the set $\{1, 2, ..., 17\}$ such that $a+b$ is a perfect square.

• Sum = 4: (1,3)
• Sum = 9: (1,8), (2