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---
title: Towers of Hanoi
id: 5951ed8945deab770972ae56
challengeType: 5
---
## Description
< section id = 'description' >
Task:
< p > Solve the < a href = "https://en.wikipedia.org/wiki/Towers_of_Hanoi" title = "wp: Towers_of_Hanoi" > Towers of Hanoi< / a > problem.< / p >
< p >
Your solution should accept the number of discs as the first parameters, and
three string used to identify each of the three stacks of discs, for example
< code > towerOfHanoi(4, 'A', 'B', 'C')< / code > . The function should return an
array of arrays containing the list of moves, source -> destination. For
example, the array < code > [['A', 'C'], ['B', 'A']]< / code > indicates that the
1st move was to move a disc from stack A to C, and the 2nd move was to move a
disc from stack B to A.
< / p >
< / section >
## Instructions
< section id = 'instructions' >
< / section >
## Tests
< section id = 'tests' >
```yml
tests:
- text: < code > towerOfHanoi</ code > is a function.
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testString: assert(typeof towerOfHanoi === 'function', '< code > towerOfHanoi< / code > is a function.');
- text: < code > towerOfHanoi(3, ...)</ code > should return 7 moves.
testString: assert(res3.length === 7, '< code > towerOfHanoi(3, ...)< / code > should return 7 moves.');
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- text: < code > towerOfHanoi(3, 'A', 'B', 'C')</ code > should return < code > [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B']]</ code >
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testString: assert.deepEqual(towerOfHanoi(3, 'A', 'B', 'C'), res3Moves, "< code > towerOfHanoi(3, 'A', 'B', 'C')< / code > should return [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B']].");
- text: < code > towerOfHanoi(5, "X", "Y", "Z")</ code > 10th move should be Y -> X.
testString: assert.deepEqual(res5[9], ['Y', 'X'], '< code > towerOfHanoi(5, "X", "Y", "Z")< / code > 10th move should be Y -> X.');
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- text: < code > towerOfHanoi(7, 'A', 'B', 'C')</ code > first ten moves are < code > [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B'],['A','C'],['B','C'],['B','A']]</ code >
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testString: assert.deepEqual(towerOfHanoi(7, 'A', 'B', 'C').slice(0, 10), res7First10Moves, "< code > towerOfHanoi(7, 'A', 'B', 'C')< / code > first ten moves are [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B'],['A','C'],['B','C'],['B','A']].");
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
function towerOfHanoi (n, a, b, c) {
// Good luck!
return [[]];
}
```
< / div >
### After Test
< div id = 'js-teardown' >
```js
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const res3 = towerOfHanoi(3, 'A', 'B', 'C');
const res3Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B']];
const res5 = towerOfHanoi(5, 'X', 'Y', 'Z');
const res7First10Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B'], ['A', 'C'], ['B', 'C'], ['B', 'A']];
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```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
function towerOfHanoi(n, a, b, c) {
const res = [];
towerOfHanoiHelper(n, a, c, b, res);
return res;
}
function towerOfHanoiHelper(n, a, b, c, res) {
if (n > 0) {
towerOfHanoiHelper(n - 1, a, c, b, res);
res.push([a, c]);
towerOfHanoiHelper(n - 1, b, a, c, res);
}
}
```
< / section >