45 lines
1.6 KiB
Markdown
45 lines
1.6 KiB
Markdown
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---
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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:Turn Callednumber Larry'smemory Larry'sscore Robin'smemory Robin'sscore 1 1 1 0 1 0 2 2 1,2 0 1,2 0 3 4 1,2,4 0 1,2,4 0 4 6 1,2,4,6 0 1,2,4,6 0 5 1 1,2,4,6 1 1,2,4,6 1 6 8 1,2,4,6,8 1 1,2,4,6,8 1 7 10 1,4,6,8,10 1 2,4,6,8,10 1 8 2 1,2,6,8,10 1 2,4,6,8,10 2 9 4 1,2,4,8,10 1 2,4,6,8,10 3 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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`euler298()` should return 1.76882294.
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```js
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assert.strictEqual(euler298(), 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 euler298() {
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return true;
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}
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euler298();
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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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