Dudeney 谜题 57

Where a large number of workmen are employed on a building it is customary to provide every man with a little disc bearing his number. These are hung on a board by the men as they arrive, and serve as a check on punctuality. Now, I once noticed a foreman remove a number of these checks from his board and place them on a split-ring which he carried in his pocket. This at once gave me the idea for a good puzzle. In fact, I will confide to my readers that this is just how ideas for puzzles arise. You cannot really create an idea: it happens—and you have to be on the alert to seize it when it does so happen. It will be seen from the illustration that there are ten of these checks on a ring, numbered 1 to 9 and 0. The puzzle is to divide them into three groups without taking any off the ring, so that the first group multiplied by the second makes the third group. For example, we can divide them into the three groups, 2—8 9 7—1 5 4 6 3, by bringing the 6 and the 3 round to the 4, but unfortunately the first two when multiplied together do not make the third. Can you separate them correctly? Of course you may have as many of the checks as you like in any group. The puzzle calls for some ingenuity, unless you have the luck to hit on the answer by chance.

当建筑物雇用大量工人时，通常会为每个人提供一个带有其编号的小圆盘。当人们到达时，它们会被挂在一块木板上，作为准时性的检查。现在，我曾经注意到一位工头从他的板上取下了一些这样的支票，并将它们放在他口袋里的开口环上。这立刻给了我一个很好的拼图的想法。事实上，我会向我的读者透露，这就是谜题创意的产生方式。你无法真正创造一个想法：它会发生——当它发生时，你必须保持警惕并抓住它。从图中可以看出，一个环上有 10 个这样的格子，编号为 1 到 9 和 0。谜题是将它们分成三组，而不将环上的任何一个取下，这样第一组乘以第二组就得到第三组。例如，我们可以将它们分成三组：2—8 9 7—1 5 4 6 3，将6和3轮带入4，但不幸的是，前两组相乘并不能得到第三组。你能正确地将它们分开吗？当然，您可以在任何组中拥有任意数量的支票。这个谜题需要一些独创性，除非你有幸偶然找到答案。