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Felix Martin
2018-02-12 00:40:11 +01:00
parent bf8af81715
commit 2f39bda323
2 changed files with 64 additions and 42 deletions
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@@ -188,6 +188,16 @@ div#notebook {
<p>Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.</p>
<p>HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.</p>
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<p>We start by thinking about how many digits are used for multiplicand/multiplier/product. Obviously, the product must have more then three digits. Can it have more then 4 digits? Obviously it can because then there are only four digits for multiplicand and multiplier which is always smaller than ten thousand. So our product must be in the form $12 \cdot 345 = 5789$. This makes the rest very easy in Python.</p>
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@@ -196,8 +206,24 @@ div#notebook {
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">permutations</span>
<span class="k">def</span> <span class="nf">is_solution</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]),</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]),</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">5</span><span class="p">:])</span>
<span class="k">if</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
<span class="k">return</span> <span class="n">c</span>
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">1</span><span class="p">]),</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">5</span><span class="p">]),</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">5</span><span class="p">:])</span>
<span class="k">if</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
<span class="k">return</span> <span class="n">c</span>
<span class="k">return</span> <span class="mi">0</span>
<span class="k">assert</span><span class="p">(</span><span class="n">is_solution</span><span class="p">(</span><span class="s2">&quot;391867254&quot;</span><span class="p">)</span> <span class="o">==</span> <span class="mi">7254</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">is_solution</span><span class="p">(</span><span class="s2">&quot;391867245&quot;</span><span class="p">)</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="nb">sum</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">is_solution</span><span class="p">(</span><span class="s2">&quot;&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">p</span><span class="p">))</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">(</span><span class="s2">&quot;123456789&quot;</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">45228</span><span class="p">)</span>
<span class="n">s</span>
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<span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">AssertionError</span> Traceback (most recent call last)
<span class="ansigreen">&lt;ipython-input-1-8e612cf3c592&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
<span class="ansigreen"> 1</span> s <span class="ansiyellow">=</span> <span class="ansicyan">0</span><span class="ansiyellow"></span>
<span class="ansigreen">----&gt; 2</span><span class="ansiyellow"> </span><span class="ansigreen">assert</span><span class="ansiyellow">(</span>s <span class="ansiyellow">==</span> <span class="ansicyan">45228</span><span class="ansiyellow">)</span><span class="ansiyellow"></span>
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<pre>45228</pre>
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