Euler 029 - Distinct powers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Euler Problem 29\n",
    "================\n",
    "\n",
    "Consider all integer combinations of $a^b$ for $2 \\le a \\le 5$ and $2 \\le b \\le 5$:\n",
    "\n",
    "$$2^2=4, 2^3=8, 2^4=16, 2^5=32$$\n",
    "$$3^2=9, 3^3=27, 3^4=81, 3^5=243$$\n",
    "$$4^2=16, 4^3=64, 4^4=256, 4^5=1024$$\n",
    "$$5^2=25, 5^3=125, 5^4=625, 5^5=3125$$\n",
    "\n",
    "If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:\n",
    "\n",
    "    4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125\n",
    "\n",
    "How many distinct terms are in the sequence generated by $a^b$ for $2 \\le a \\le 100$ and $2\\le b\\le 100$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9183\n"
     ]
    }
   ],
   "source": [
    "print(len(set(a**b for a in range(2,101) for b in range(2,101))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternative solution using itertools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9183\n"
     ]
    }
   ],
   "source": [
    "from itertools import product\n",
    "print(len(set(a**b for a, b in product(range(2, 101), repeat=2))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}