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Tried to solve 55 till 57.

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Felix Martin
2018-12-24 17:15:19 -05:00
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<p>A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.</p>
<p>Considering natural numbers of the form, ab, where a, b &lt; 100, what is the maximum digital sum?</p>
<p>A googol ($10^{100}$) is a massive number: one followed by one-hundred zeros; $100^{100}$ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.</p>
<p>Considering natural numbers of the form, $a^b$, where $a, b &lt; 100$, what is the maximum digital sum?</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">get_digit_sum</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">n</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">s</span> <span class="o">+=</span> <span class="p">(</span><span class="n">n</span> <span class="o">%</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">n</span> <span class="o">//=</span> <span class="mi">10</span>
<span class="k">return</span> <span class="n">s</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_digit_sum</span><span class="p">(</span><span class="mi">1337</span><span class="p">)</span> <span class="o">==</span> <span class="mi">14</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_digit_sum</span><span class="p">(</span><span class="mi">100</span><span class="o">**</span><span class="mi">100</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="n">get_digit_sum</span><span class="p">(</span><span class="n">a</span><span class="o">**</span><span class="n">b</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</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">100</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</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">100</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>972
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