66 lines
2.0 KiB
Markdown
66 lines
2.0 KiB
Markdown
---
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id: 5900f4591000cf542c50ff6b
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title: 'Problem 236: Luxury Hampers'
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challengeType: 5
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forumTopicId: 301881
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dashedName: problem-236-luxury-hampers
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---
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# --description--
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Suppliers 'A' and 'B' provided the following numbers of products for the luxury hamper market:
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| Product | 'A' | 'B' |
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|--------------------|------|------|
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| Beluga Caviar | 5248 | 640 |
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| Christmas Cake | 1312 | 1888 |
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| Gammon Joint | 2624 | 3776 |
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| Vintage Port | 5760 | 3776 |
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| Champagne Truffles | 3936 | 5664 |
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Although the suppliers try very hard to ship their goods in perfect condition, there is inevitably some spoilage - i.e. products gone bad.
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The suppliers compare their performance using two types of statistic:
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- The five per-product spoilage rates for each supplier are equal to the number of products gone bad divided by the number of products supplied, for each of the five products in turn.
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- The overall spoilage rate for each supplier is equal to the total number of products gone bad divided by the total number of products provided by that supplier.
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To their surprise, the suppliers found that each of the five per-product spoilage rates was worse (higher) for 'B' than for 'A' by the same factor (ratio of spoilage rates), $m > 1$; and yet, paradoxically, the overall spoilage rate was worse for 'A' than for 'B', also by a factor of $m$.
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There are thirty-five $m > 1$ for which this surprising result could have occurred, the smallest of which is $\frac{1476}{1475}$.
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What's the largest possible value of $m$? Give your answer as a string with fraction reduced to its lowest terms, in the form `u/v`.
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# --hints--
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`luxuryHampers()` should return a string.
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```js
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assert(typeof luxuryHampers() === 'string');
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```
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`luxuryHampers()` should return the string `123/59`.
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```js
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assert.strictEqual(luxuryHampers(), '123/59');
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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 luxuryHampers() {
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return true;
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}
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luxuryHampers();
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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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