### Brain Teasers

# Squares and What?

What to do these numbers have in common, besides being perfect squares?

1) 25

2) 100

3) 169

4) 225

1) 25

2) 100

3) 169

4) 225

### Hint

25 = 16 + 9100 = 36 + 64

### Answer

All of these are expressible in the form a*a=b*b+c*c:1) 25 = 4*4+3*3

2) 100 = 6*6+8*8

3) 169 = 12*12+5*5

4) 225 = 12*12+9*9

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## Comments

I liked this teaser!

And, I don't really get why its difficulty rating is so high since the hint gives it away.

And, I don't really get why its difficulty rating is so high since the hint gives it away.

I had the same basic idea, just represented as another consequence of the same property.

All of these are a solution for X where (X - Y), X, (X + Y) each of the three vslues is a square number and X and Y are non-zero integers:

(25 - 24) = 1^2, 25 = 5^2, (25 + 24) = 7 ^2

(100 - 96) = 2^2, 100 = 10^2, (100 + 96) = 14^2

(169 - 120) = 7^2, 169 = 13^2, (169 + 120) = 17 ^2

(225 - 216) = 3^2, 225 = 15^2, (225 + 216) = 21^2

All of these are a solution for X where (X - Y), X, (X + Y) each of the three vslues is a square number and X and Y are non-zero integers:

(25 - 24) = 1^2, 25 = 5^2, (25 + 24) = 7 ^2

(100 - 96) = 2^2, 100 = 10^2, (100 + 96) = 14^2

(169 - 120) = 7^2, 169 = 13^2, (169 + 120) = 17 ^2

(225 - 216) = 3^2, 225 = 15^2, (225 + 216) = 21^2

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