60 lines
1.4 KiB
Markdown
60 lines
1.4 KiB
Markdown
---
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id: 5900f3ca1000cf542c50fedc
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title: 'Problem 93: Arithmetic expressions'
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challengeType: 5
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forumTopicId: 302210
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dashedName: problem-93-arithmetic-expressions
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---
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# --description--
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By using each of the digits from the set, {1, 2, 3, 4}, exactly once, and making use of the four arithmetic operations (+, −, \*, /) and brackets/parentheses, it is possible to form different positive integer targets.
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For example,
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<div style='margin-left: 4em;'>
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8 = (4 * (1 + 3)) / 2<br>
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14 = 4 * (3 + 1 / 2)<br>
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19 = 4 * (2 + 3) − 1<br>
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36 = 3 * 4 * (2 + 1)
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</div>
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Note that concatenations of the digits, like 12 + 34, are not allowed.
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Using the set, {1, 2, 3, 4}, it is possible to obtain thirty-one different target numbers of which 36 is the maximum, and each of the numbers 1 to 28 can be obtained before encountering the first non-expressible number.
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Find the set of four distinct digits, `a` < `b` < `c` < `d`, for which the longest set of consecutive positive integers, 1 to `n`, can be obtained, giving your answer as a string: `abcd`.
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# --hints--
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`arithmeticExpressions()` should return a number.
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```js
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assert(typeof arithmeticExpressions() === 'number');
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```
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`arithmeticExpressions()` should return 1258.
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```js
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assert.strictEqual(arithmeticExpressions(), 1258);
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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 arithmeticExpressions() {
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return true;
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}
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arithmeticExpressions();
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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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