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一九八四年“五·四”青年智力竞赛有这样一个题:“一元一张的人民币换零,至多有多少种换法?”本文将巧妙地用确定线性不定方程式非负整数解的个数的方法迅速获得了此题准确无误的答案,并用此法解决了二元、五元、十元一张钞票换零的最多方案种数问题。现介绍于后。解:设一元一张人民币兑换成票额为1分、2分、5分、1角、2角、5角的人民币分别为x_1、x_2、x_3、x_4、x_5、x_6张,依题
The “May 4th” youth quiz in 1984 contained the following question: “How many conversions can there be at most one Yuan RMB exchange for zero?” This article will skillfully use the non-negative integer solution to determine the linear indefinite equation. The number method quickly obtained the correct answer to this question and used this method to solve the problem of the maximum number of zeros for binary, five, and ten dollar notes. Now introduced in the post. Solution: Set RMB 1 to RMB 1, 2, 5, 1, 1, 2 and 5 RMB as x_1, x_2, x_3, x_4, x_5, x_6, respectively.