Sums of Squares: Upper Primary Mathematics Competition Question

Alice is playing a number game. She is trying to make every whole number as the sum of square numbers. For example, 14 = 3² + 2² + 1² and 15 = 3² + 2² + 1² + 1².

But she notices that numbers like 14 can be made using all different squares, whereas others, like 15, need to use the same square number twice. Indeed, some numbers may need to use the same square three times.

Now, can you find those numbers between 20 and 30 inclusive that can be made as the sum of different squares?

It doesn't matter how many squares you use - it could be two, three or four, or even just one!



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