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广东省廉江市的读者严健来信如下: “请编辑部帮助解答: 1．证明:不能在圆周上放置数1,2,3, …,12,13,使得相邻两个数之差的绝对值均 为3,4,5之一,但能放置1,2,…,13,14 使之满足要求． 2．求不定方程x+y+z+w=20满足x≤ 6,y≤7,x≤8,w≤9的正整数解的组数． 这两题我很久也未能解决,希望编辑部 给我答复．” 编辑部给出如下的解答供读者参考．
The reader of Jianjian, Lianjiang City, Guangdong Province, wrote as follows: “Please help the editorial office to help answer: 1. Proof: You cannot place numbers 1,2,3,...,12,13 on the circumference so that the difference between two adjacent numbers The absolute value is one of 3,4,5, but can be placed 1,2,...,13,14 to meet the requirements. 2. The indefinite equation x+y+z+w=20 satisfies x≤ 6,y≤ The number of groups of positive integer solutions for 7, x ≤ 8, w ≤ 9 has been a long time ago. I hope the editorial department can give me a reply. The editorial department gives the following answers for readers’ reference.