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Cycling Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

William from Tattingstone School said that he tried four times before he came up with a solution to Cycling Squares:

15-10-6-313-12-4-5-11-14-2-34-30-19-17-8-28-21

We're glad you didn't give up, William. Beth and Pheobe from Exminster CP School and Skye and Molly from Breckland Middle School also used trial and error (or trial and improvement as I like to call it!). Beth and Phoebe said it tested their skills of perseverance.

Matha, also from Tattingstone, said that she started with the number $2$ and then added $14$ because it was the only number she could have added to make a square number. She goes on to say:

I then added $11$ to $14$ to get $25$ which is another square number and carried on like this.

Martha sent in a drawing of her circle which is the same as William's answer, just written in a different way:

circle of numbers going clockwise: 14, 11, 5, 4, 17, 13, 3, 6, 10, 15, 21, 28, 8, 17, 19, 30, 34, 2

.

Dominic from Stonehill took a logical approach:


I listed the numbers and wrote down their pairs to make square numbers.
Some of the numbers only had two possible combinations to make square numbers, so I started with one of these. I put in $2$ first and put $14$ and $34$ on either side of it.
From there, I put $11$ on the other side of the $14$ as these were the only combinations, and so on.
Some numbers had four or even five possible combinations but by trial and error I moved these around until all the combinations made a square number.

Brandon, Antonia and Oliver from Mayhill Junior used a similar method to Dominic. Emilie and Bethany from Alverstoke Junior School said:

To solve the problem we first worked out the highest square number was $64$.
We then worked out all the square numbers from $4$ to $64$.
We then worked out which pairs of numbers made square numbers and we used trial and error to solve the problem.

Very well done to you all.