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Euler has design of a homepage and there is a link back to the overview for each solution.

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Felix Martin
2018-06-14 20:11:26 -04:00
parent 894160d1a0
commit c34ebd6181
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<title>EulerProblem006</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="Euler-Problem-6">Euler Problem 6<a class="anchor-link" href="#Euler-Problem-6">&#182;</a></h1><p>The sum of the squares of the first ten natural numbers is,</p>
<h1 id="Euler-Problem-6">Euler Problem 6<a class="anchor-link" href="#Euler-Problem-6"></a></h1><p><a href="/euler">Back to overview.</a></p><p>The sum of the squares of the first ten natural numbers is,</p>
<p>$1^2 + 2^2 + ... + 10^2 = 385$</p>
<p>The square of the sum of the first ten natural numbers is,</p>
<p>$(1 + 2 + ... + 10)^2 = 55^2 = 3025$</p>
<p>Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is $3025 − 385 = 2640$.</p>
<p>Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.</p>
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<p>Okay, this is as straightforward as it can get.</p>
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<div class="prompt input_prompt">In&nbsp;[1]:</div>
<div class="prompt input_prompt">In [1]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">101</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">101</span><span class="p">)])</span>
<span class="k">assert</span><span class="p">(</span><span class="n">s</span> <span class="o">==</span> <span class="mi">25164150</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
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<pre>25164150
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<p>General solution.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">diff_between_sum_of_squares_and_square_sum</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)])</span>
<span class="k">assert</span><span class="p">(</span><span class="n">diff_between_sum_of_squares_and_square_sum</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span> <span class="o">==</span> <span class="mi">25164150</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">diff_between_sum_of_squares_and_square_sum</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2640</span><span class="p">)</span>
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