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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-426-box-ball-system.md

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+---
+id: 5900f5171000cf542c510029
+challengeType: 5
+title: 'Problem 426: Box-ball system'
+forumTopicId: 302096
+---
+
+## Description
+<section id='description'>
+Consider an infinite row of boxes. Some of the boxes contain a ball. For example, an initial configuration of 2 consecutive occupied boxes followed by 2 empty boxes, 2 occupied boxes, 1 empty box, and 2 occupied boxes can be denoted by the sequence (2, 2, 2, 1, 2), in which the number of consecutive occupied and empty boxes appear alternately.
+
+
+A turn consists of moving each ball exactly once according to the following rule: Transfer the leftmost ball which has not been moved to the nearest empty box to its right.
+
+
+After one turn the sequence (2, 2, 2, 1, 2) becomes (2, 2, 1, 2, 3) as can be seen below; note that we begin the new sequence starting at the first occupied box.
+
+
+
+
+
+
+A system like this is called a Box-Ball System or BBS for short.
+
+
+It can be shown that after a sufficient number of turns, the system evolves to a state where the consecutive numbers of occupied boxes is invariant. In the example below, the consecutive numbers of occupied boxes evolves to [1, 2, 3]; we shall call this the final state.
+
+
+
+
+
+
+We define the sequence {ti}:s0 = 290797
+sk+1 = sk2 mod 50515093
+tk = (sk mod 64) + 1
+
+Starting from the initial configuration (t0, t1, …, t10), the final state becomes [1, 3, 10, 24, 51, 75].
+Starting from the initial configuration (t0, t1, …, t10 000 000), find the final state.
+Give as your answer the sum of the squares of the elements of the final state. For example, if the final state is [1, 2, 3] then 14 ( = 12 + 22 + 32) is your answer.
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>euler426()</code> should return 31591886008.
+    testString: assert.strictEqual(euler426(), 31591886008);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function euler426() {
+
+  return true;
+}
+
+euler426();
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+```js
+// solution required
+```
+
+</section>