Challenge 1
We drew the first 5 centred squares to find them.
They are 1, 5, 13, 25 and 41.
Challenge 2
We noticed that to get the next centred square you add four more each time.
The 9th number would be 1 + 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32
which is the same as 1 + (1 x 4) + (2 x 4) + (3 x 4) + (4 x 4) + (5 x 4) + (6 x 4) + (7 x 4) + (8 x 4)
If you add them together that makes 1 + (36 x 4) = 145
Challenge 3
We worked out the first 9 centred square numbers are 1, 5, 13, 25, 41, 61, 85, 113, 145
Max then carried on with the challenges.
He started with 145 because it is closest to the total.
211 - 145 = 66
You can make 66 using 61 + 5 or 41 + 25 so 211 is 145 + 61 + 5 or 145 + 41 + 25
To get 212 you can just add 1 so 145 + 61 + 5 + 1 or 145 + 41 + 25 + 1
213 - 145 = 68 and we couldn’t find a way to make 68 so tried starting with 113 instead.
213 - 113 = 100
100 - 61 = 39
39 - 25 = 14
1 + 13 + 25 + 61 + 113 = 213