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 Going Digital With Pythagoras (Posted on 2008-11-08)
Determine all possible list(s) of pythagorean triple (a,b,c), with 0 < a < b < c < 100, such that we will obtain another pythagorean triple (p,q,r) by inserting the same nonzero digit to the left of each of a, b and c. None of a, b and c can contain any leading zeroes.

Note: Try to derive a non computer assisted method, although computer program/spreadsheet solutions are welcome.

 See The Solution Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 3

FOR a = 1 TO 98
FOR b = a + 1 TO 99
FOR c = b + 1 TO 100
IF a * a + b * b = c * c THEN
FOR i = 1 TO 9
ia = VAL(LTRIM\$(STR\$(i)) + LTRIM\$(STR\$(a)))
ib = VAL(LTRIM\$(STR\$(i)) + LTRIM\$(STR\$(b)))
ic = VAL(LTRIM\$(STR\$(i)) + LTRIM\$(STR\$(c)))
IF ia * ia + ib * ib = ic * ic THEN PRINT a; b; c, i
NEXT
END IF
NEXT
NEXT
NEXT

finds

5  12  13

with the appropriate digit prefix being a 1.

 Posted by Charlie on 2008-11-08 17:12:49

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