chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f4a11000cf542c50ffb4
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title: 问题309:整数阶梯
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title: 'Problem 309: Integer Ladders'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 301963
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dashedName: problem-309-integer-ladders
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---
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# --description--
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在经典的“穿越梯子”问题中,我们得到了两个梯子的长度x和y,它们位于一条狭窄的水平街道的相对壁上。 我们还给出了两个梯子交叉的街道上方的高度h,并要求我们找到街道的宽度(w)。
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In the classic "Crossing Ladders" problem, we are given the lengths x and y of two ladders resting on the opposite walls of a narrow, level street. We are also given the height h above the street where the two ladders cross and we are asked to find the width of the street (w).
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在这里,我们仅关注所有四个变量均为正整数的实例。 例如,如果x = 70,y = 119,h = 30,我们可以计算出w = 56。
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Here, we are only concerned with instances where all four variables are positive integers. For example, if x = 70, y = 119 and h = 30, we can calculate that w = 56.
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实际上,对于x,y,h和0 <x <y <200的整数,只有五个三元组(x,y,h)产生w的整数解: (70、119、30),(74、182、21),(87、105、35),(100、116、35)和(119、175、40)。
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In fact, for integer values x, y, h and 0 < x < y < 200, there are only five triplets (x,y,h) producing integer solutions for w: (70, 119, 30), (74, 182, 21), (87, 105, 35), (100, 116, 35) and (119, 175, 40).
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对于整数值x,y,h和0 <x <y <1 000 000,有多少个三元组(x,y,h)产生w的整数解?
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For integer values x, y, h and 0 < x < y < 1 000 000, how many triplets (x,y,h) produce integer solutions for w?
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# --hints--
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`euler309()`应该返回210139。
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`euler309()` should return 210139.
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```js
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assert.strictEqual(euler309(), 210139);
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