Question

George has 32 beads, each engraved with a number from 1-32 without repetition.

He wants to create a circular chain by connecting all these beads in a way, such that the sum of the numbers of any two adjacent beads make a perfect square.

How should he place the beads to create the chain?

Answer 1

Answer:

He should place the beads by 25 ways

Step-by-step explanation:

1+8 = 9 = 3^2

8 + 28 = 36 = 9^2

28 + 21 = 49 = 7^2

and so on...

26+10 = 36 = 9^2

10+15 = 25 = 5^2

15+ 1 = 16 = 4^2

Answer 2

Answer:

$1-8-28-21- 4-32-17-19-30-6-3-13-12-24-25-11-5-31-18-7-29-20-16-9-27-22-14-2-23-26-10-15$

Step-by-step explanation:

The following is the arrangement of numbers from 1-32 without repeating, arranged in such a way the the sum of any two adjacent numbers is a perfect square.

$1-8-28-21- 4-32-17-19-30-6-3-13-12-24-25-11-5-31-18-7-29-20-16-9-27-22-14-2-23-26-10-15$

To make a circle of this arrangement just connect last number 15 to first number 1, that makes a circle.