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Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Reasonable Algebra

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Have you noticed that in the picture for 4+5+6+7+8+9+10 the rectangle has an even length and an odd height

How about a diagram representing 8+9+10+11+12+13+14+15+16+17?
What can you say about the length and height of the rectangle in this case?

Is there a general rule?