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「Ants on a Square」.

Ants on a Square #

Problem #

There are $51$ ants on a square with a side length of $1$. If you have a glass with a radius of $\frac{1}{7}$, can you place your glass at a position on the square to guarantee that the glass encompasses at least $3$ ants?

Solution 1 #

考虑使用抽屉原理. 总共有 $51$ 只蚂蚁, 想让至少一个抽屉有三只蚂蚁, 至多有 $25$ 个抽屉. 考虑将正方形分成 $25$ 个边长为 $\frac{1}{5}$ 的小正方形, 而半径为 $\frac{1}{7}$ 的圆可以覆盖一个边长为 $\frac{1}{5}$ 的小正方形.