Problem #PRU-65194

Problems Discrete Mathematics Combinatorics Dissections, partitions, covers and tilings Dissections with certain properties Methods Pigeonhole principle Pigeonhole principle (area and volume)

14–15 4.0

Problem

Every day, James bakes a square cake size $3 \times 3$ . Jack immediately cuts out for himself four square pieces of size $1 \times 1$ with sides parallel to the sides of the cake (not necessarily along the $3 \times 3$ grid lines). After that, Sarah cuts out from the rest of the cake a square piece with sides, also parallel to the sides of the cake. What is the largest piece of cake that Sarah can count on, regardless of Jack’s actions?

To see the solution register and get verified.