103 lines
2.6 KiB
Plaintext
103 lines
2.6 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Coded triangle numbers (Euler Problem 42)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The nth term of the sequence of triangle numbers is given by, $t_n = \\frac{1}{2}n(n+1)$; so the first ten triangle numbers are:\n",
|
|
"\n",
|
|
" 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\n",
|
|
"\n",
|
|
"By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = $t_{10}$. If the word value is a triangle number then we shall call the word a triangle word.\n",
|
|
"\n",
|
|
"Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words? (The file is saved in the same directory as this notebook file as EulerProblem042.txt)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def get_words():\n",
|
|
" with open(\"EulerProblem042.txt\", \"r\") as f:\n",
|
|
" s = f.read()\n",
|
|
" words = [w.strip('\"') for w in s.split(\",\")]\n",
|
|
" return words\n",
|
|
"\n",
|
|
"def calculate_word_value(word):\n",
|
|
" word = word.upper()\n",
|
|
" return sum([ord(letter) - 64 for letter in word])\n",
|
|
"\n",
|
|
"assert(calculate_word_value(\"sky\") == 55)\n",
|
|
"\n",
|
|
"def get_triangle_numbers(n):\n",
|
|
" return {n * (n + 1) // 2 for n in range(1, 101)}"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"162\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"triangle_numbers = get_triangle_numbers(100)\n",
|
|
"\n",
|
|
"s = len([word for word in get_words() if calculate_word_value(word) in triangle_numbers])\n",
|
|
"assert(s == 162)\n",
|
|
"print(s)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"completion_date": "Thu, 20 Dec 2018, 16:14",
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python3.6",
|
|
"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": "3.6.5"
|
|
},
|
|
"tags": [
|
|
"triangle",
|
|
"words"
|
|
]
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|