2014-09-24

# Problem 039: Integer right triangles

Description:

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ? 1000, is the number of solutions maximised?

Solution:
v
>010p020p630p"d"55+*90p050p30g3/70p         v
vp07/3g03p050                                                    p03+2<
v                     >#        v# p07-1<           >10p30g20pv
>30g::270g*-*\70g-2*%#^_50g1+50p>70g:2-#^_\$50g:10g`#^_\$       >30g:90g-|
>                             \$^\$          <                    @.g02\$<
Start
??
Pause
Reset
Output:
Stack:   (0)

Explanation:

We have the two formulas `a^2 + b^2 = c^2` and `a + b + c = p`. We can insert the second in the first and get `b = p*(p-2a) / 2*(p-a)` and `c = p-(b+a)`.
The we just go through all possible values for a and p and test if b is an integer. Then we search for the value of p with the most possible values of a.

 Interpreter steps: 3 815 878 Execution time (BefunExec): 827ms (4.61 MHz) Program size: 72 x 6 (fully conform befunge-93) Solution: 840 Solved at: 2014-09-24

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