This was quite a difficult problem - particularly the explanation at the end. Caroline from Tattingstone sent in her ideas:

The first prime number which is greater than 3 is 5 so I got 5 and squared it which is 25 then I took away 1 and got 24.
The next prime number is 7. I squared it and got 49 then I took away 1 which is 48.
The next prime number is 11. I squared it and got 121 then I took away 1 and got 120.

So Caroline had the numbers 24, 48 and 120. She then said:

I notice that 24 goes into all three numbers. It goes into 24 once, 48 twice and 120 five times.

Caroline tried a few more:

13² = 169 169 - 1 = 168 168 = 7 x 24
17² = 289 289 - 1 = 288 288 = 12 x 24
19² = 361 361 - 1 = 360 360 = 15 x 24

Very well done Caroline.

Rachael, Pandora, Anna, Emily, Zarah, Ben and James all in Year 6 at Ardingly College spotted the fact that all the numbers are multiples of 24 too. I wonder whether anyone could try to explain why this is?