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番外 · 题谱 · 1917 · P5

Amusement 11 · Tiled Yard 11

几何趣题 · P2/P5 · 中段题

题面摘自 Henry E. Dudeney 公版文本;英文为古腾堡原文整理,中文为本站自译,提示、解答骨架和闲谈保留本站原创结构。

Amusements in Mathematics 1917 11 geometric

'Twas last Bank Holiday, so I've been told, Some cyclists rode abroad in glorious weather. Resting at noon within a tavern old, They all agreed to have a feast together. "Put it all in one bill, mine host," they said, "For every man an equal share will pay." The bill was promptly on the table laid, And four pounds was the reckoning that day. But, sad to state, when they prepared to square, 'Twas found that two had sneaked outside and fled. So, for two shillings more than his due share Each honest man who had remained was bled. They settled later with those rogues, no doubt. How many were they when they first set out?

“去年银行假期,有人告诉我,一些骑自行车的人在晴朗的天气里骑车出国。中午在一家老酒馆里休息,大家约定一起吃顿饭。 “主人,把这一切都写在一张账单上,”他们说,“每个人都将得到平等的份额。”帐单很快就摆在桌子上,当天的计算结果是四英镑。但遗憾的是,当他们准备摆好姿势时,却发现其中有两个人偷偷溜到外面逃跑了。因此,为了比他应得的份额多出两先令,每个留下来的诚实人都流血了。毫无疑问,他们后来与那些盗贼和解了。他们第一次出发时有多少人?

提示 1

先把图画成可量的对象,标出边、格点或切割线。

提示 2

找面积、长度、对称轴或不变量,不急着剪。

提示 3

若是重排题,检查每一块在移动前后是否保持形状和面积。

完整解答

把题目先放到方格纸上。若四块面积相等,每块面积是总面积的四分之一;“轮廓相同”要求两道切割线在旋转或翻折后能互相对应。解题主线是先画出中心对称或四分旋转的候选,再用方格计数核对每块面积。

Dudeney 的趣题常把难点藏在“看起来可以试”的地方。别急着猜答案;先把图、表或状态画出来,再问哪些限制一直没有变。这也是它和 Carroll 逻辑题互补的地方:一个拆句子,一个拆结构。