---
id: 599d1566a02b571412643b84
title: Ethiopian multiplication
challengeType: 5
forumTopicId: 302257
dashedName: ethiopian-multiplication
---
# --description--
Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
**Method:**
- Take two numbers to be multiplied and write them down at the top of two columns
- 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
1
- 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
1
- Examine the table produced and discard any row where the value in the left column is even
- Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
**For example:** `17 × 34`
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So `17` multiplied by `34`, by the Ethiopian method is `578`.
# --instructions--
The task is to define three named functions/methods/procedures/subroutines:
- one to halve an integer,
- one to double an integer, and
- one to state if an integer is even
Use these functions to create a function that does Ethiopian multiplication.
# --hints--
`eth_mult` should be a function.
```js
assert(typeof eth_mult === 'function');
```
`eth_mult(17,34)` should return `578`.
```js
assert.equal(eth_mult(17, 34), 578);
```
`eth_mult(23,46)` should return `1058`.
```js
assert.equal(eth_mult(23, 46), 1058);
```
`eth_mult(12,27)` should return `324`.
```js
assert.equal(eth_mult(12, 27), 324);
```
`eth_mult(56,98)` should return `5488`.
```js
assert.equal(eth_mult(56, 98), 5488);
```
`eth_mult(63,74)` should return `4662`.
```js
assert.equal(eth_mult(63, 74), 4662);
```
# --seed--
## --seed-contents--
```js
function eth_mult(a, b) {
}
```
# --solutions--
```js
function eth_mult(a, b) {
let sum = 0; a = [a]; b = [b];
let half = a => a / 2,
double = a => a * 2,
is_even = a => a % 2 == 0;
while (a[0] !== 1) {
a.unshift(Math.floor(half(a[0])));
b.unshift(double(b[0]));
}
for (let i = a.length - 1; i > 0; i -= 1) {
if (!is_even(a[i])) {
sum += b[i];
}
}
return sum + b[0];
}
```