PyPE solution to PE problem 9
Registered by
Scott Armitage
PyPE solution to PE problem 9
Blueprint information
- Status:
- Complete
- Approver:
- None
- Priority:
- Undefined
- Drafter:
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- Direction:
- Needs approval
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- Definition:
- Approved
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- Implementation:
-
Implemented
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- Started by
- Scott Armitage
- Completed by
- Scott Armitage
Whiteboard
ProjectEule
===
A Pythagorean triplet is a set of three natural numbers, a b c, for which
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Solution
--------
We begin with some properties of right triangles, where c is the hypotenuse.
We know that a+b+c=p (1) and a+b>c (2). Adding c to both sides of (2) and
substituting into (1) we see that p>2c.
Since p=1000, we have that c<=500, and since it is the longest side, we
also have that a<=500 and b<= 500.
Answer
------
31875000
(?)
