# Project Euler in R Problem 9

**Frank Portman**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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In Problem 9 of Project Euler we are tasked with finding the product (a*b*c) of the Pythagorean Triplet (a, b, c) such that a + b + c = 1000.

A Pythagorean triplet is a set of three natural numbers such that a^{2} + b^{2} = c^{2}.

To solve this problem, we first see that c = (a^{2} + b^{2})^{1/2}. Without loss of generality, we can only run the for loop for a and b, since c will be uniquely determined given a certain a and b.

The code I used:

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<span class="line"><span class="kr">for</span> <span class="p">(</span>a <span class="kr">in</span> <span class="m">1</span><span class="o">:</span><span class="m">499</span><span class="p">)</span> <span class="p">{</span> </span><span class="line"> <span class="kr">for</span> <span class="p">(</span>b <span class="kr">in</span> <span class="m">1</span><span class="o">:</span><span class="m">499</span><span class="p">)</span> <span class="p">{</span> </span><span class="line"> <span class="kr">if</span> <span class="p">(</span>a <span class="o">+</span> b <span class="o">+</span> <span class="kp">sqrt</span><span class="p">(</span>a<span class="o">^</span><span class="m">2</span> <span class="o">+</span> b<span class="o">^</span><span class="m">2</span><span class="p">)</span> <span class="o">==</span> <span class="m">1000</span><span class="p">)</span> <span class="p">{</span> </span><span class="line"> <span class="kp">print</span><span class="p">(</span>a <span class="o">*</span> b <span class="o">*</span> <span class="kp">sqrt</span><span class="p">(</span>a<span class="o">^</span><span class="m">2</span> <span class="o">+</span> b<span class="o">^</span><span class="m">2</span><span class="p">))</span> </span><span class="line"> <span class="kr">break</span> </span><span class="line"> <span class="p">}</span> </span><span class="line"> <span class="p">}</span> </span><span class="line"> <span class="kr">if</span> <span class="p">(</span>a <span class="o">+</span> b <span class="o">+</span> <span class="kp">sqrt</span><span class="p">(</span>a<span class="o">^</span><span class="m">2</span> <span class="o">+</span> b<span class="o">^</span><span class="m">2</span><span class="p">)</span> <span class="o">==</span> <span class="m">1000</span><span class="p">)</span> <span class="p">{</span> </span><span class="line"> <span class="kr">break</span> </span><span class="line"> <span class="p">}</span> </span><span class="line"><span class="p">}</span> </span> |

I use nested for loops to test values of a and b between 1 and 499. a and b cannot take values greater than 499 because then a + b + sqrt(a^{2} + b^{2}) would be greater than 1000.

The if statement in the nested loops checks to see whether a, b, and c add up to 1000. If they do, it prints their product and then breaks the loop. This is a short script which produces the correct answer in a few milliseconds. The trick here was expressing c in terms of a and b to reduce the amount of loops we need to run.

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**Frank Portman**.

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