ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
47 lines
1.5 KiB
Markdown
47 lines
1.5 KiB
Markdown
---
|
|
id: 5900f49f1000cf542c50ffb1
|
|
title: 'Problem 306: Paper-strip Game'
|
|
challengeType: 5
|
|
forumTopicId: 301960
|
|
dashedName: problem-306-paper-strip-game
|
|
---
|
|
|
|
# --description--
|
|
|
|
The following game is a classic example of Combinatorial Game Theory:
|
|
|
|
Two players start with a strip of n white squares and they take alternate turns. On each turn, a player picks two contiguous white squares and paints them black. The first player who cannot make a move loses.
|
|
|
|
If n = 1, there are no valid moves, so the first player loses automatically. If n = 2, there is only one valid move, after which the second player loses. If n = 3, there are two valid moves, but both leave a situation where the second player loses. If n = 4, there are three valid moves for the first player; she can win the game by painting the two middle squares. If n = 5, there are four valid moves for the first player (shown below in red); but no matter what she does, the second player (blue) wins.
|
|
|
|
So, for 1 ≤ n ≤ 5, there are 3 values of n for which the first player can force a win. Similarly, for 1 ≤ n ≤ 50, there are 40 values of n for which the first player can force a win.
|
|
|
|
For 1 ≤ n ≤ 1 000 000, how many values of n are there for which the first player can force a win?
|
|
|
|
# --hints--
|
|
|
|
`euler306()` should return 852938.
|
|
|
|
```js
|
|
assert.strictEqual(euler306(), 852938);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler306() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler306();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|