136 lines
3.5 KiB
Markdown
136 lines
3.5 KiB
Markdown
---
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title: Ethiopian multiplication
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id: 599d1566a02b571412643b84
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challengeType: 5
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---
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## Description
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<section id='description'>
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Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
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<strong>Method:</strong>
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<ol>
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<li>Take two numbers to be multiplied and write them down at the top of two columns</li>
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<li>In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of <code>1</code></li>
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<li>In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows <code>1</code></li>
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<li>Examine the table produced and discard any row where the value in the left column is even</li>
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<li>Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together</li>
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</ol>
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<strong>For example:</strong> <code>17 × 34</code>
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<pre>
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17 34
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</pre>
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Halving the first column:
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<pre>
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17 34
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8
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4
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2
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1
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</pre>
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Doubling the second column:
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<pre>
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17 34
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8 68
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4 136
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2 272
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1 544
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</pre>
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Strike-out rows whose first cell is even:
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<pre>
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17 34
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8 <strike>68</strike>
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4 <strike>136</strike>
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2 <strike>272</strike>
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1 544
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</pre>
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Sum the remaining numbers in the right-hand column:
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<pre>
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17 34
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8 --
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4 ---
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2 ---
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1 544
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====
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578
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</pre>
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So <code>17</code> multiplied by <code>34</code>, by the Ethiopian method is <code>578</code>.
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</section>
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## Instructions
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<section id='instructions'>
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The task is to define three named functions/methods/procedures/subroutines:
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<ol>
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<li>one to halve an integer,</li>
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<li>one to double an integer, and</li>
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<li>one to state if an integer is even</li>
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</ol>
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Use these functions to create a function that does Ethiopian multiplication.
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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>eth_mult</code> is a function.
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testString: assert(typeof eth_mult === 'function', '<code>eth_mult</code> is a function.');
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- text: <code>eth_mult(17,34)</code> should return <code>578</code>.
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testString: assert.equal(eth_mult(17, 34), 578, '<code>eth_mult(17,34)</code> should return <code>578</code>.');
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- text: <code>eth_mult(23,46)</code> should return <code>1058</code>.
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testString: assert.equal(eth_mult(23, 46), 1058, '<code>eth_mult(23,46)</code> should return <code>1058</code>.');
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- text: <code>eth_mult(12,27)</code> should return <code>324</code>.
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testString: assert.equal(eth_mult(12, 27), 324, '<code>eth_mult(12,27)</code> should return <code>324</code>.');
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- text: <code>eth_mult(56,98)</code> should return <code>5488</code>.
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testString: assert.equal(eth_mult(56, 98), 5488, '<code>eth_mult(56,98)</code> should return <code>5488</code>.');
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- text: <code>eth_mult(63,74)</code> should return <code>4662</code>.
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testString: assert.equal(eth_mult(63, 74), 4662, '<code>eth_mult(63,74)</code> should return <code>4662</code>.');
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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 eth_mult(a, b) {
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// Good luck!
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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 eth_mult(a, b) {
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let sum = 0; a = [a]; b = [b];
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let half = a => a / 2,
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double = a => a * 2,
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is_even = a => a % 2 == 0;
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while (a[0] !== 1) {
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a.unshift(Math.floor(half(a[0])));
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b.unshift(double(b[0]));
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}
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for (let i = a.length - 1; i > 0; i -= 1) {
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if (!is_even(a[i])) {
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sum += b[i];
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}
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}
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return sum + b[0];
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}
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```
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</section>
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