397a9f0c3e
* fix: clean-up Project Euler 462-480 * fix: missing image extension * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
60 lines
1.2 KiB
Markdown
60 lines
1.2 KiB
Markdown
---
|
||
id: 5900f53e1000cf542c510051
|
||
title: 'Problem 466: Distinct terms in a multiplication table'
|
||
challengeType: 5
|
||
forumTopicId: 302141
|
||
dashedName: problem-466-distinct-terms-in-a-multiplication-table
|
||
---
|
||
|
||
# --description--
|
||
|
||
Let $P(m,n)$ be the number of distinct terms in an $m×n$ multiplication table.
|
||
|
||
For example, a 3×4 multiplication table looks like this:
|
||
|
||
$$\begin{array}{c}
|
||
× & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} \\\\
|
||
\mathbf{1} & 1 & 2 & 3 & 4 \\\\
|
||
\mathbf{2} & 2 & 4 & 6 & 8 \\\\
|
||
\mathbf{3} & 3 & 6 & 9 & 12
|
||
\end{array}$$
|
||
|
||
There are 8 distinct terms {1, 2, 3, 4, 6, 8, 9, 12}, therefore $P(3, 4) = 8$.
|
||
|
||
You are given that:
|
||
|
||
$$\begin{align}
|
||
& P(64, 64) = 1\\,263, \\\\
|
||
& P(12, 345) = 1\\,998, \text{ and} \\\\
|
||
& P(32, {10}^{15}) = 13\\,826\\,382\\,602\\,124\\,302. \\\\
|
||
\end{align}$$
|
||
|
||
Find $P(64, {10}^{16})$.
|
||
|
||
# --hints--
|
||
|
||
`multiplicationTable()` should return `258381958195474750`.
|
||
|
||
```js
|
||
assert.strictEqual(multiplicationTable(), 258381958195474750);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function multiplicationTable() {
|
||
|
||
return true;
|
||
}
|
||
|
||
multiplicationTable();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|