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Oliver Eyton-Williams
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---
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title: 24 game
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id: 5951e88f64ebf159166a1176
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challengeType: 5
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forumTopicId: 302218
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---
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## Description
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<section id='description'>
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The <a href="https://en.wikipedia.org/wiki/24_Game" target="_blank">24 Game</a> tests a person's mental arithmetic.
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The aim of the game is to arrange four numbers in a way that when evaluated, the result is 24
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</section>
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## Instructions
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<section id='instructions'>
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Implement a function that takes a string of four digits as its argument, with each digit from 1 to 9 (inclusive) with repetitions allowed, and returns an arithmetic expression that evaluates to the number 24. If no such solution exists, return "no solution exists".
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<h4><strong>Rules:</strong></h4>
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<ul>
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<li> Only the following operators/functions are allowed: multiplication, division, addition, subtraction. </li>
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<li> Division should use floating point or rational arithmetic, etc, to preserve remainders. </li>
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<li> Forming multiple digit numbers from the supplied digits is disallowed. (So an answer of 12+12 when given 1, 2, 2, and 1 is wrong). </li>
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<li> The order of the digits when given does not have to be preserved. </li>
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</ul>
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| Example input | Example output |
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| --- | --- |
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| <code>solve24("4878");</code> | <code>(7-8/8)*4</code> |
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| <code>solve24("1234");</code> | <code>3*1*4*2</code> |
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| <code>solve24("6789");</code> | <code>(6*8)/(9-7)</code> |
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| <code>solve24("1127");</code> | <code>(1+7)*(2+1)</code> |
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>solve24</code> should be a function.
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testString: assert(typeof solve24 === 'function');
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- text: <code>solve24("4878")</code> should return <code>(7-8/8)*4</code> or <code>4*(7-8/8)</code>
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testString: assert(include(answers[0], removeParentheses(solve24(testCases[0]))));
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- text: <code>solve24("1234")</code> should return any arrangement of <code>1*2*3*4</code>
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testString: assert(include(answers[1], removeParentheses(solve24(testCases[1]))));
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- text: <code>solve24("6789")</code> should return <code>(6*8)/(9-7)</code> or <code>(8*6)/(9-7)</code>
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testString: assert(include(answers[2], removeParentheses(solve24(testCases[2]))));
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- text: <code>solve24("1127")</code> should return a permutation of <code>(1+7)*(1+2)</code>
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testString: assert(include(answers[3], removeParentheses(solve24(testCases[3]))));
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function solve24 (numStr) {
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return true;
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const testCases = [
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'4878',
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'1234',
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'6789',
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'1127'
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];
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const answers = [
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['(7-8/8)*4', '4*(7-8/8)', '(4-8+7)*8', '(4+7-8)*8', '(7+4-8)*8', '(7-8+4)*8', '8*(4-8+7)', '8*(4+7-8)', '8*(7+4-8)', '8*(7-8+4)'],
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['1*2*3*4', '1*2*4*3', '1*3*2*4', '1*3*4*2', '1*4*2*3', '1*4*3*2', '2*1*3*4', '2*1*4*3', '2*3*1*4', '2*3*4*1', '2*4*3*1', '2*4*1*3', '3*1*2*4', '3*1*4*2', '3*2*1*4', '3*2*4*1', '3*4*1*2', '3*4*2*1', '4*1*2*3', '4*1*3*2', '4*2*1*3', '4*2*3*1', '4*3*1*2', '4*3*2*1', '(1+2+3)*4', '(1+3+2)*4', '(2+1+3)*4', '(2+3+1)*4', '(3+1+2)*4', '(3+2+1)*4', '4*(1+2+3)', '4*(2+1+3)', '4*(2+3+1)', '4*(3+1+2)', '4*(3+2+1)'],
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['(6*8)/(9-7)', '(8*6)/(9-7)', '6*8/(9-7)', '8*6/(9-7)'],
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['(1+7)*(2+1)', '(1+7)*(1+2)', '(1+2)*(1+7)', '(1+2)*(7+1)', '(2+1)*(1+7)', '(7+1)*(2+1)']
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];
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function include(ansArr, res) {
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const index = ansArr.indexOf(res);
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return index >= 0;
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}
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//The main method for detecting single parentheses
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function removeParentheses(ans) {
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for (let i = 0; i < ans.length; i++) {
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if (!isNaN(ans[i])) {
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ans = removeParenthesesHelper(ans, i);
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}
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}
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return ans;
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}
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//Helper to remove left and right parantheses
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function removeParenthesesHelper(ans, i) {
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while (i > 0 && i < ans.length - 1) {
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if (ans[i - 1] === '(' && ans[i + 1] === ')') {
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//Paranthesis detected. Remove them.
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ans = replaceChar(ans, '', i - 1);
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ans = replaceChar(ans, '', i);
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i--;
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} else {
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return ans;
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}
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}
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return ans;
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}
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//Replace a character at a given index for the provided character
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function replaceChar(origString, replaceChar, index) {
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let firstPart = origString.substr(0, index);
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let lastPart = origString.substr(index + 1);
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let newString = firstPart + replaceChar + lastPart;
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return newString;
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function solve24(numStr) {
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const digitsArr = numStr.split('');
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const answers = [];
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const digitPermutations = [];
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const operatorPermutations = [];
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function generateDigitPermutations (digits, permutations = []) {
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if (digits.length === 0) {
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digitPermutations.push(permutations);
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}
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else {
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for (let i = 0; i < digits.length; i++) {
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const curr = digits.slice();
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const next = curr.splice(i, 1);
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generateDigitPermutations(curr.slice(), permutations.concat(next));
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}
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}
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}
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function generateOperatorPermutations (permutations = []) {
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const operators = ['+', '-', '*', '/'];
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if (permutations.length === 3) {
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operatorPermutations.push(permutations);
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}
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else {
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for (let i = 0; i < operators.length; i++) {
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const curr = permutations.slice();
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curr.push(operators[i]);
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generateOperatorPermutations(curr);
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}
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}
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}
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generateDigitPermutations(digitsArr);
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generateOperatorPermutations();
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interleave();
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return answers[0];
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function interleave () {
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for (let i = 0; i < digitPermutations.length; i++) {
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for (let j = 0; j < operatorPermutations.length; j++) {
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const d = digitPermutations[i];
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const o = operatorPermutations[j];
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const perm = [
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`${d[0]}${o[0]}${d[1]}${o[1]}${d[2]}${o[2]}${d[3]}`,
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`(${d[0]}${o[0]}${d[1]})${o[1]}${d[2]}${o[2]}${d[3]}`,
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`${d[0]}${o[0]}(${d[1]}${o[1]}${d[2]})${o[2]}${d[3]}`,
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`${d[0]}${o[0]}${d[1]}${o[1]}(${d[2]}${o[2]}${d[3]})`,
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`${d[0]}${o[0]}(${d[1]}${o[1]}${d[2]}${o[2]}${d[3]})`,
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`(${d[0]}${o[0]}${d[1]}${o[1]}${d[2]})${o[2]}${d[3]}`,
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`(${d[0]}${o[0]}${d[1]})${o[1]}(${d[2]}${o[2]}${d[3]})`
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];
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perm.forEach(combination => {
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const res = eval(combination);
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if (res === 24) {
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return answers.push(combination);
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}
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});
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}
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}
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}
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}
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```
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</section>
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