PUMaC 2013 · 代数（B 组） · 第 2 题
PUMaC 2013 — Algebra (Division B) — Problem 2
题目详情
- [ 3 ] Betty Lou and Peggy Sue take turns flipping switches on a 100 × 100 grid. Initially, all switches are “off.” Betty Lou always flips a horizontal row of switches on her turn; Peggy Sue always flips a vertical column of switches. When they finish, there is an odd number of switches turned “on” in each row and column. Find the maximum number of switches that can be on, in total, when they finish.
解析
- If there are 2 real roots, then there are 6 possibilities for their product. There are 3 2 possibilities for the remaining t − 2 xt + 1 factor, namely x ∈ { 0 , ± 1 / 2 } . Thus there are 18 possibilities for f .