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William from Tattingstone School said that he tried four times before he came up with a solution to Cycling Squares:
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:
Dominic from Stonehill took a logical approach:
Brandon, Antonia and Oliver from Mayhill Junior used a similar method to Dominic. Emilie and Bethany from Alverstoke Junior School said:
Very well done to you all. Here are some comments we received in 2015 from pupils at Queen Edith, Cambridge having completed the challenge.Edward:- "I worked it out by using trial and improvement and it took us a couple of times to figure it out. I started with one pair of numbers and went both ways around the circle"
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?