SOLUTION: Three numbers between 100 and 150 can each be expressed as the sum of two different squares in two different ways. What is the sum of the three numbers?

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These three numbers are


    125 = 2^2 + 11^2 = 5^2 + 10^2,


    130 = 3^2 + 11^2 = 7^2 + 9^2,


    145 = 1^2 + 12^2 = 8^2 + 9^2.


Their sum is  125 + 130 + 145 = 400.    ANSWER