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

2018-06-14 20:11:26 -04:00
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-<h1 id="Euler-Problem-16">Euler Problem 16<a class="anchor-link" href="#Euler-Problem-16">&#182;</a></h1><p>$2^{15}$ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.</p>
+<h1 id="Euler-Problem-16">Euler Problem 16<a class="anchor-link" href="#Euler-Problem-16">¶</a></h1><p><a href="/euler">Back to overview.</a></p><p>$2^{15}$ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.</p>
 <p>What is the sum of the digits of the number $2^{1000}$?</p>
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 <p>Seriously? Okay, probably more difficult in C.</p>
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-<div class="prompt input_prompt">In&nbsp;[17]:</div>
+<div class="prompt input_prompt">In [17]:</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="nb">map</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">str</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">1000</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">1366</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>1366
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 <p>Okay, let's do it without big ints.</p>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">double_number_string</span><span class="p">(</span><span class="n">number_string</span><span class="p">):</span>
    <span class="n">number_string</span> <span class="o">=</span> <span class="n">number_string</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># reverse</span>
    <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
@@ -11848,77 +11831,61 @@ div#notebook {
        <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">next_digit</span><span class="p">))</span>
    <span class="k">if</span> <span class="n">carriage</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
        <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">carriage</span><span class="p">))</span>
-    <span class="n">result</span> <span class="o">=</span> <span class="s2">&quot;&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">result</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+    <span class="n">result</span> <span class="o">=</span> <span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">result</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
    <span class="k">return</span> <span class="n">result</span>

-<span class="k">assert</span><span class="p">(</span><span class="n">double_number_string</span><span class="p">(</span><span class="s2">&quot;132&quot;</span><span class="p">)</span> <span class="o">==</span> <span class="s2">&quot;264&quot;</span><span class="p">)</span>
-<span class="k">assert</span><span class="p">(</span><span class="n">double_number_string</span><span class="p">(</span><span class="s2">&quot;965&quot;</span><span class="p">)</span> <span class="o">==</span> <span class="s2">&quot;1930&quot;</span><span class="p">)</span>
+<span class="k">assert</span><span class="p">(</span><span class="n">double_number_string</span><span class="p">(</span><span class="s2">"132"</span><span class="p">)</span> <span class="o">==</span> <span class="s2">"264"</span><span class="p">)</span>
+<span class="k">assert</span><span class="p">(</span><span class="n">double_number_string</span><span class="p">(</span><span class="s2">"965"</span><span class="p">)</span> <span class="o">==</span> <span class="s2">"1930"</span><span class="p">)</span>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">powers_of_two</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot; Retuns nth power of two as a string. &quot;&quot;&quot;</span>
+    <span class="sd">""" Retuns nth power of two as a string. """</span>
    <span class="k">assert</span><span class="p">(</span><span class="n">n</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-        <span class="k">return</span> <span class="s2">&quot;1&quot;</span>
-    <span class="n">s</span> <span class="o">=</span> <span class="s2">&quot;2&quot;</span>
+        <span class="k">return</span> <span class="s2">"1"</span>
+    <span class="n">s</span> <span class="o">=</span> <span class="s2">"2"</span>
    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</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="n">s</span> <span class="o">=</span> <span class="n">double_number_string</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">s</span>

-<span class="k">assert</span><span class="p">(</span><span class="n">powers_of_two</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">==</span> <span class="s2">&quot;8&quot;</span><span class="p">)</span>
-<span class="k">assert</span><span class="p">(</span><span class="n">powers_of_two</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="o">==</span> <span class="s2">&quot;1024&quot;</span><span class="p">)</span>
+<span class="k">assert</span><span class="p">(</span><span class="n">powers_of_two</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">==</span> <span class="s2">"8"</span><span class="p">)</span>
+<span class="k">assert</span><span class="p">(</span><span class="n">powers_of_two</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="o">==</span> <span class="s2">"1024"</span><span class="p">)</span>

 <span class="n">number_string</span> <span class="o">=</span> <span class="n">powers_of_two</span><span class="p">(</span><span class="mi">1000</span><span class="p">)</span>
 <span class="nb">print</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">number_string</span><span class="p">)))</span>
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 <pre>1366
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 <p>Here we go. The conversion to integer and the sum would be easy in C.</p>
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