Question 174
A rectangular grid of size $7 \times 9$ is given (see the figure). In the bottom-left vertex of the grid there is a colony of ants, and in the top-right vertex there is their anthill. In every other vertex of the grid there is one grain of rice. Each ant from the colony walks to the anthill along the edges of the grid, but only in the directions right or up. On its way it picks up all the grains of rice it meets, and when it reaches the anthill it stays there. What is the smallest number of ants the colony must contain so that they can pick up all the grains of rice?
