Sunday, January 14, 2007

Cranes and Tortoises

Recently I have been into arithmetic, a primary mathematics which is taught in most cram schools for the elementary school's students proposing to the prestigious junior-high schools in Japan. Don't make light of it! It is harder than we might first expect.

One of famous problems in arithmetic is on figuring the number of cranes and tortoises from the total of their legs. We call it a "crane-tortoise figure". (However I can't find the official translation of it.) This problem originally comes from a Chinese old math book written in more than 1,500 years ago. See the following problem:

The total number of cranes and tortoises that we have is 8. And the total of their legs is 26. When cranes have two legs and tortoises four legs, answer the number of cranes and of tortoises respectively.

By the way, I posted another problem related to a "crane-tortoise figure", an age figure. Of course, because it is a problem of arithmetic that the children under 12 would try, you mustn't solve it by using the first-order equation. Let's have a try!

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