51 lines
2.0 KiB
Markdown
51 lines
2.0 KiB
Markdown
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---
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id: 5900f4ba1000cf542c50ffcd
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title: 'Problem 334: Spilling the beans'
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challengeType: 5
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forumTopicId: 301992
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dashedName: problem-334-spilling-the-beans
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---
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# --description--
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In Plato's heaven, there exist an infinite number of bowls in a straight line. Each bowl either contains some or none of a finite number of beans. A child plays a game, which allows only one kind of move: removing two beans from any bowl, and putting one in each of the two adjacent bowls. The game ends when each bowl contains either one or no beans.
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For example, consider two adjacent bowls containing 2 and 3 beans respectively, all other bowls being empty. The following eight moves will finish the game:
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<img class="img-responsive center-block" alt="animation of game when two adjacent bowls contains 2 and 3 beans respectivelly" src="https://cdn.freecodecamp.org/curriculum/project-euler/spilling-the-beans.gif" style="background-color: white; padding: 10px;" />
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You are given the following sequences:
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$$\begin{align} & t_0 = 123456, \\\\ & t_i = \begin{cases} \frac{t_{i - 1}}{2}, & \text{if $t_{i - 1}$ is even} \\\\ \left\lfloor\frac{t_{i - 1}}{2}\right\rfloor \oplus 926252, & \text{if $t_{i - 1}$ is odd} \end{cases} \\\\ & \qquad \text{where $⌊x⌋$ is the floor function and $\oplus$ is the bitwise XOR operator.} \\\\ & b_i = (t_i\bmod 2^{11}) + 1. \end{align}$$
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The first two terms of the last sequence are $b_1 = 289$ and $b_2 = 145$. If we start with $b_1$ and $b_2$ beans in two adjacent bowls, 3419100 moves would be required to finish the game.
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Consider now 1500 adjacent bowls containing $b_1, b_2, \ldots, b_{1500}$ beans respectively, all other bowls being empty. Find how many moves it takes before the game ends.
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# --hints--
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`spillingTheBeans()` should return `150320021261690850`.
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```js
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assert.strictEqual(spillingTheBeans(), 150320021261690850);
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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 spillingTheBeans() {
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return true;
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}
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spillingTheBeans();
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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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