Solved problem 40.

ipython/EulerProblem040.ipynb

@@ -0,0 +1,118 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Champernowne's constant (Euler Problem 40)\n",
+    "\n",
+    "<https://projecteuler.net/problem=40>\n",
+    "\n",
+    "An irrational decimal fraction is created by concatenating the positive integers:\n",
+    "\n",
+    "    0.123456789101112131415161718192021...\n",
+    "\n",
+    "It can be seen that the 12th digit of the fractional part is 1.\n",
+    "\n",
+    "If dn represents the nth digit of the fractional part, find the value of the following expression.\n",
+    "\n",
+    "$d_{1} × d_{10} × d_{100} × d_{1000} × d_{10000} × d_{100000} × d_{1000000}$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "I do not see why we cannot hold $8 bytes \\times 10^{6} = 8 MB$ in memory."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_irrational_fraction(digits_max):\n",
+    "    s = []\n",
+    "    n = 1\n",
+    "    digits = 0\n",
+    "    while digits < digits_max:\n",
+    "        s.append(str(n))\n",
+    "        digits += len(str(n))\n",
+    "        n += 1\n",
+    "    return \"\".join(s)\n",
+    "\n",
+    "assert(get_irrational_fraction(20)[12] == \"1\")\n",
+    "\n",
+    "f = get_irrational_fraction(1000001)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Okay, we got the fractional. No we get the digits at the different positions and calculate the product. For that purpose we reuse our poduct function from problem 8."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def product(xs):\n",
+    "    from operator import mul\n",
+    "    from functools import reduce\n",
+    "    return reduce(mul, xs, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "210\n"
+     ]
+    }
+   ],
+   "source": [
+    "s = product(map(int, [f[10**i - 1] for i in range(7)]))\n",
+    "print(s)\n",
+    "assert(s == 210)"
+   ]
+  }
+ ],
+ "metadata": {
+  "completion_date": "Sun, 20 May 2018, 00:40",
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python3.5",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  },
+  "tags": [
+   "champernowne",
+   "product",
+   "fraction"
+  ]
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}