Finished 32 in ipython.

ipython/EulerProblem032.html

@@ -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>
 
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<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>
+
 </div>
 </div>
 </div>
@@ -196,8 +206,24 @@ div#notebook {
 <div class="prompt input_prompt">In&nbsp;[1]:</div>
 <div class="inner_cell">
     <div class="input_area">
-<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>
 </pre></div>
 
 </div>
@@ -208,32 +234,15 @@ div#notebook {
 <div class="output">
 
 
-<div class="output_area"><div class="prompt"></div>
-<div class="output_subarea output_text output_error">
-<pre>
-<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>
+<div class="output_area"><div class="prompt output_prompt">Out[1]:</div>
 
-<span class="ansired">AssertionError</span>: </pre>
-</div>
+
+<div class="output_text output_subarea output_execute_result">
+<pre>45228</pre>
 </div>
 
-</div>
 </div>
 
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython3"><pre><span></span> 
-</pre></div>
-
-</div>
 </div>
 </div>
 

ipython/EulerProblem032.ipynb

@@ -15,6 +15,13 @@
     "HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "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."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 1,
@@ -23,30 +30,36 @@
    },
    "outputs": [
     {
-     "ename": "AssertionError",
-     "evalue": "",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
-      "\u001b[1;32m<ipython-input-1-8e612cf3c592>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m45228\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[1;31mAssertionError\u001b[0m: "
-     ]
+     "data": {
+      "text/plain": [
+       "45228"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "s = 0\n",
-    "assert(s == 45228)"
+    "from itertools import permutations\n",
+    "\n",
+    "def is_solution(s):\n",
+    "    a, b, c = int(s[0:2]), int(s[2:5]), int(s[5:])\n",
+    "    if a * b == c:\n",
+    "        return c\n",
+    "    a, b, c = int(s[0:1]), int(s[1:5]), int(s[5:])  \n",
+    "    if a * b == c:\n",
+    "        return c\n",
+    "    return 0\n",
+    "\n",
+    "assert(is_solution(\"391867254\") == 7254)\n",
+    "assert(is_solution(\"391867245\") == 0)\n",
+    "\n",
+    "\n",
+    "s = sum(set([is_solution(\"\".join(p)) for p in permutations(\"123456789\")]))\n",
+    "assert(s == 45228)\n",
+    "s"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {