Question 11
2011 storehouses are connected by roads so that every storehouse is reachable from every other. Storehouse $i$ contains $x_i$ kg of cement. One trip may transport any amount along a direct road. The target is $y_i$ kg at storehouse $i$, with $\sum x_i=\sum y_i$. Find the least $N$ guaranteeing completion in $N$ trips for every admissible distribution and road system.