Both questions are of the first level algebra. The linear simultaneous equation is taught at middle schools for 12 years old children.
(1) Let X be the number of the rolls of cloths and Y be the number of thieves. X = 7Y + 8 = 8Y - 7 Hence, Y = 15 X = 7 x 15 + 8 = 113 (2) Let X be the number of the rolls of cloths and Y be the number of thieves. X = 5Y + 3 = 6Y - 5 Hence, Y = 8 X = 5 x 8 + 3 = 43 I bet the ancient Chinese used something other than X and Y. Minoru Mochizuki ----- Original Message ----- From: Mark Spahn To: not_honyaku Sent: Sunday, October 12, 2008 10:33 PM Subject: nusubito-zan (thieves' reckoning) As sometimes happens, while looking for something else in a dictionary, I ran across something more interesting than the original search quarry. There is a kind of dividing-the-spoils problem known as 盗人算 (nusubito-zan, or "thieves' calculation"). A Japanese dictionary gives its origin as the Chinese 「孫子算経」（三、四世紀）. Here is the kind of problem it refers to: 絹盗人が、盗んだ反物を分け合っている。 「７反ずつ取れば８反余り、８反ずつ取れば７反足らず。」 盗人の人数と、反物の数はいくつでしょう。 Silk thieves are overheard dividing their stolen loot. "If each of us gets 7 rolls of cloth, 8 rolls will be left over, and if each is to get 8 rolls, we are 7 rolls short." How many thieves are there, and how many rolls of cloth did they steal? -- Mark Spahn (West Seneca, NY) Another example, in which unseen bolts-of-cloth thieves are overheard: 旅人が道に迷って、夜になったのでお堂の中に入って寝ることにした。 真夜中に、外から話し声が聞こえるので、聞き耳を立てていると、 反物泥棒達が、反物の分け方を相談していた。 「５反（たん）ずつ分けると３反あまる。」 「６反ずつ分けると、５反たりない。 "If each of us takes 5, 3 will be left over." "If each of us is to have 6, we'll need 5 more." 泥棒の人数は何人で、反物（たんもの）は何反だろう。 --~--~---------~--~----~------------~-------~--~----~ Persons posting messages to not_honyaku assume all responsibility for their messages. The list owner does not review messages, and accepts no responsibility for the content of messages posted. -~----------~----~----~----~------~----~------~--~---
