The Lemon Fool

This puzzle was in something my son got from school. It's not as hard as your normal puzzles but I enjoyed doing it so I shall share:

Place the following numbers in a ring such that the sum of two adjacent numbers is a square number. You may only use each number once.
2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 17, 19, 21, 28, 30, 34

I guess you could show them as a list with an implicit pairing from the head to the tail.

- Rover

Rover110 wrote:This puzzle was in something my son got from school. It's not as hard as your normal puzzles but I enjoyed doing it so I shall share:

Place the following numbers in a ring such that the sum of two adjacent numbers is a square number. You may only use each number once.
2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 17, 19, 21, 28, 30, 34

I guess you could show them as a list with an implicit pairing from the head to the tail.

- Rover

Spoiler:

The possible sums of squares within the required range are 9,16,25,36,49,64.
Starting with 2, we can see it can only be combined with 14 or 34 to sum to a square number; they will be the neighbours of 2 in the ring.
The remainder of the ring can be found in the same way, giving:

2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 21, 28, 8, 17, 19, 30, 34

Hi GS. You got it in one (I think there's only one solution, other than rotations / mirror-image). Hope you enjoyed it.

- Rover

I got the answer although I think I made rather heavy weather of the solution. But it was a good puzzle. Do you have any more like this? They don't have to be hard.

Cinelli