2010-05-04 18:21:07 +00:00
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"""Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.
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A Pythagorean triplet is a set of three natural numbers, a b c, for which,
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a2 + b2 = c2
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For example, 32 + 42 = 9 + 16 = 25 = 52.
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There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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Find the product abc.
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"""
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2010-04-12 15:53:07 +00:00
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TRIPLET_SUM = 1000
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2010-05-04 18:21:07 +00:00
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def main():
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for c in range(TRIPLET_SUM - 3, 3, -2):
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diff = TRIPLET_SUM - c
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for x in range(1, int(diff / 2) + 1):
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(a, b) = (x, diff - x)
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if a**2 + b**2 == c**2:
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print '{a}**2 + {b}**2 == {c}**2'.format(a=a, b=b, c=c)
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print 'Product: ', a*b*c
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if __name__ == '__main__':
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main()
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