Delete Cheryl's Birthday.ipynb
This commit is contained in:
Peter Norvig
GitHub
parent
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commit
11db599107
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"When is Cheryl's Birthday?\n",
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"===\n",
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"\n",
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"[This puzzle](https://www.google.com/webhp?#q=cheryl%27s%20birthday) has been making the rounds:\n",
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"\n",
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"1. Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gave them a list of 10 possible dates:\n",
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"<pre>\n",
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" May 15 May 16 May 19\n",
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" June 17 June 18\n",
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" July 14 July 16\n",
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" August 14 August 15 August 17\n",
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"</pre>\n",
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" \n",
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"2. Cheryl then tells Albert and Bernard separately the month and the day of the birthday resepctively.\n",
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" \n",
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"3. Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\n",
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" \n",
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"4. Bernard: At first I don't know when Cheryl's birthday is, but I know now.\n",
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" \n",
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"5. Albert: Then I also know when Cheryl's birthday is.\n",
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" \n",
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"6. So when is Cheryl's birthday?\n",
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"\n",
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"\n",
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"\n",
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"1. Cheryl gave them a list of 10 possible dates:\n",
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"---\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"DATES = ['May 15', 'May 16', 'May 19',\n",
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" 'June 17', 'June 18',\n",
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" 'July 14', 'July 16',\n",
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" 'August 14', 'August 15', 'August 17']"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We'll define accessor functions for the month and day of a date:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def Month(date): return date.split()[0]\n",
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"\n",
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"def Day(date): return date.split()[1]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'May'"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"Month('May 15')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'15'"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"Day('May 15')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"2. Cheryl then tells Albert and Bernard separately the month and the day of the birthday respectively.\n",
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"---\n",
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"\n",
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"We can define the idea of **telling**, and while we're at it, the idea of **knowing** a birthdate:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def tell(part, possible_dates=DATES):\n",
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" \"Cheryl tells a part of her birthdate to someone; return a new list of possible dates that match the part.\"\n",
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" return [date for date in possible_dates if part in date]\n",
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"\n",
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"def know(possible_dates):\n",
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" \"A person knows the birthdate if they have exactly one possible date.\"\n",
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" return len(possible_dates) == 1"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Note that we use a *list of dates* to represent someone's knowledge of the possible birthdates, and that someone *knows* the birthdate when they get down to only one possibility. For example: If Cheryl tells Albert that her birthday is in May, he would know there is a list of three possible birthdates:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"['May 15', 'May 16', 'May 19']"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"tell('May')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"And if she tells Bernard that her birthday is on the 15th, he would know there are two possibilities:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"['May 15', 'August 15']"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"tell('15')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"With two possibilities, Bernard does not know the birthdate:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"False"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"know(tell('15'))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Overall Strategy\n",
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"---\n",
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"\n",
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"When Cheryl tells Albert `'May'` then *he* knows there are three possibilities, but *we* (the puzzle solvers) don't, because we don't know what Cheryl said. So what can we do? We will consider *all* of the possible dates, one at a time. For example, first consider `'May 15'`. Cheryl tells Albert `'May'` and Bernard `'15'`, giving them the lists of possible birthdates shown above. We can then check whether statements 3 through 5 are true in this scenario. If they are, then `'May 15'` is a solution to the puzzle. Repeat the process for each of the other possible dates. If all goes well, there should be exactly one solution. \n",
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"\n",
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"Here is the main function, `cheryls_birthday`:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def cheryls_birthday(possible_dates=DATES):\n",
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" \"Return a list of the possible dates for which all three statements are true.\"\n",
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" return filter(all3, possible_dates)\n",
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"\n",
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"def all3(date): return statement3(date) and statement4(date) and statement5(date)\n",
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"\n",
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"## TO DO: define statement3, statement4, statement5"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" (*Python note:* `filter(predicate, items)` returns a list of all items for which `predicate(item)` is true.)\n",
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" \n",
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" 3. Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\n",
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The function `statement3` takes as input a possible birthdate and returns true if Albert's statement is true for that birthdate. How do we go from Albert's English statement to a Python function? Let's paraphrase in a form that is closer to Python code:\n",
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"\n",
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"> **Albert**: After Cheryl told me the month of her birthdate, I didn't know her birthday. I also don't know what day Cheryl told Bernard, but for *any* of the possible dates, if Bernard was told the day of that date, he would not know Cheryl's birthday.\n",
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"\n",
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"That I can translate directly into code:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def statement3(date):\n",
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" \"Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\"\n",
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" possible_dates = tell(Month(date))\n",
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" return (not know(possible_dates) \n",
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" and all(not know(tell(Day(d)))\n",
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" for d in possible_dates))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We haven't solved the puzzle yet, but let's take a peek and see which dates satisfy statement 3:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"['July 14', 'July 16', 'August 14', 'August 15', 'August 17']"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"filter(statement3, DATES)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"4. Bernard: At first I don't know when Cheryl's birthday is, but I know now.\n",
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"---\n",
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"\n",
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"Again, a paraphrase:\n",
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"\n",
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"> **Bernard:** At first Cheryl told me the day, and I didn't know. Then I considered just the dates for which Albert's statement 3 is true, and now I know."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def statement4(date):\n",
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" \"Bernard: At first I don't know when Cheryl's birthday is, but I know now.\"\n",
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" at_first = tell(Day(date))\n",
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" return (not know(at_first) \n",
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" and know(filter(statement3, at_first)))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's see which dates satisfy both statement 3 and statement 4:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"['July 16', 'August 15', 'August 17']"
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]
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},
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"execution_count": 13,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"filter(statement4, filter(statement3, DATES))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Wait a minute—I thought that Bernard **knew**?! Why are there three possible dates? Bernard does indeed know; it is just that we, the puzzle solvers, don't know. That's because Bernard knows something we don't know: the day. We won't know until after statement 5.\n",
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"\n",
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"5. Albert: Then I also know when Cheryl's birthday is.\n",
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"---\n",
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"\n",
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"Albert is saying that after hearing the month and Bernard's statement 4, he now knows Cheryl's birthday:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def statement5(date):\n",
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" \"Albert: Then I also know when Cheryl's birthday is.\"\n",
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" return know(filter(statement4, tell(Month(date))))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"6. So when is Cheryl's birthday?\n",
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"---\n",
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"\n",
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"Let's see:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"['July 16']"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"cheryls_birthday()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Success!** We have deduced that Cheryl's birthday is **July 16**. It is now `True` that we know Cheryl's birthday:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"know(cheryls_birthday())"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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