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Three Concatenations (Posted on 2024-03-15) Difficulty: 3 of 5
Determine three positive integers A, B and C such that the concatenations AB, AC and BC are all squares, and the sum A+B+C is also a square.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution Computer solution | Comment 2 of 4 |
Searching integers up to 10,000 I found only one solution:
(A, B, C): (108, 16, 900)

√10816 = 104
√108900 = 330
√16900 = 130
√(108 + 16 + 900) = √1024 = 32
------------
big = 10000

for a in range(1,big):
    for b in range(1,big):
        if not issquare(int(str(a)+str(b))):
            continue
        for c in range(1,big):
            if not issquare(a+b+c):
                continue
            if not issquare(int(str(a)+str(c))):
                continue
            if not issquare(int(str(b)+str(c))):
                continue
            print(a,b,c)


  Posted by Larry on 2024-03-15 12:49:34
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