A Practical Guide To Quantitative Finance Interviews 收录了一些量化面试中的经典题目. 本文介绍的是来自第二章的「Clock Pieces」.

Clock Pieces #

Problem #

A clock (numbered $1$-$12$ clockwise) fell off the wall and broke into three pieces. You find that the sums of the numbers on each piece are equal. What are the numbers on each piece? (No strange-shaped piece is allowed.)

Solution 1 #

由于时钟被分成了三部分, 每部分数字之和为 $\frac{1 + 2 + … + 12}{3} = 26$ , 而 $5 + 6 + 7 + 8 = 26$ , 这可以作为一部分. 考虑表盘上其他连续的数字和为 $26$ , 有 $11 + 12 + 1 + 2 = 26$ . 剩下来的数字是 $3, 4, 9, 10$ , 其实是可能的, 因为时钟摔成了三块, 此时 $3, 4, 9, 10$ 是有可能在同一部分上的.