47fc3c6761
* fix: clean-up Project Euler 281-300 * fix: missing image extension * fix: missing power Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing subscript Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
58 lines
2.4 KiB
Markdown
58 lines
2.4 KiB
Markdown
---
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id: 5900f4971000cf542c50ffa9
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title: 'Problem 298: Selective Amnesia'
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challengeType: 5
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forumTopicId: 301950
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dashedName: problem-298-selective-amnesia
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---
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# --description--
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Larry and Robin play a memory game involving of a sequence of random numbers between 1 and 10, inclusive, that are called out one at a time. Each player can remember up to 5 previous numbers. When the called number is in a player's memory, that player is awarded a point. If it's not, the player adds the called number to his memory, removing another number if his memory is full.
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Both players start with empty memories. Both players always add new missed numbers to their memory but use a different strategy in deciding which number to remove: Larry's strategy is to remove the number that hasn't been called in the longest time. Robin's strategy is to remove the number that's been in the memory the longest time.
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Example game:
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| Turn | Called number | Larry's memory | Larry's score | Robin's memory | Robin's score |
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|------|---------------|---------------:|---------------|----------------|---------------|
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| 1 | 1 | 1 | 0 | 1 | 0 |
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| 2 | 2 | 1,2 | 0 | 1,2 | 0 |
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| 3 | 4 | 1,2,4 | 0 | 1,2,4 | 0 |
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| 4 | 6 | 1,2,4,6 | 0 | 1,2,4,6 | 0 |
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| 5 | 1 | 1,2,4,6 | 1 | 1,2,4,6 | 1 |
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| 6 | 8 | 1,2,4,6,8 | 1 | 1,2,4,6,8 | 1 |
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| 7 | 10 | 1,4,6,8,10 | 1 | 2,4,6,8,10 | 1 |
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| 8 | 2 | 1,2,6,8,10 | 1 | 2,4,6,8,10 | 2 |
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| 9 | 4 | 1,2,4,8,10 | 1 | 2,4,6,8,10 | 3 |
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| 10 | 1 | 1,2,4,8,10 | 2 | 1,4,6,8,10 | 3 |
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Denoting Larry's score by $L$ and Robin's score by $R$, what is the expected value of $|L - R|$ after 50 turns? Give your answer rounded to eight decimal places using the format x.xxxxxxxx .
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# --hints--
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`selectiveAmnesia()` should return `1.76882294`.
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```js
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assert.strictEqual(selectiveAmnesia(), 1.76882294);
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```
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# --seed--
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## --seed-contents--
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```js
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function selectiveAmnesia() {
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return true;
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}
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selectiveAmnesia();
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```
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# --solutions--
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```js
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// solution required
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```
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