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老式指针钟表盘裂成三块

old style analogue clock falls off

专题
Brainteaser / 脑筋急转弯
难度
L2

题目详情

一只老式指针钟从墙上掉下来，表盘碎成三块。每一块上包含的数字之和都相同。

描述这三块分别包含哪些数字。

英文原题

An old style analogue clock falls off the wall and the face breaks into three pieces. The numbers on each piece add to the same total. Describe the pieces.

解析

钟面数字 11 到 1212 的总和为

1+2+⋯+12=78.1+2+\cdots+12=78.

碎成三块且每块数字和相同，则每块数字和必须是

783=26.\frac{78}{3}=26.

给出一种可行分法（每组数字和都为 26）：

  • 第 1 块：{11,12,1,2}\{11,12,1,2\}（和为 26）
  • 第 2 块：{5,6,7,8}\{5,6,7,8\}（和为 26）
  • 第 3 块：{3,4,9,10}\{3,4,9,10\}（和为 26）

英文解析

The sum of the numbers 11 to 1212 on a clock face is

1+2+⋯+12=78.1+2+\cdots+12=78.

If the numbers are broken into three pieces with equal sums, then the sum of the numbers in each piece must be

783=26.\frac{78}{3}=26.

Here is a feasible partition (where the sum of numbers in each group is 26):

  • Piece 1: {11,12,1,2}\{11,12,1,2\} (sum is 26)
  • Piece 2: {5,6,7,8}\{5,6,7,8\} (sum is 26)
  • Piece 3: {3,4,9,10}\{3,4,9,10\} (sum is 26)