MathDB

Professor Oak is feeding his

100

Pokémon. Each Pokémon has a bowl whose capacity is a positive real number of kilograms. These capacities are known to Professor Oak. The total capacity of all the bowls is

100

kilograms. Professor Oak distributes

100

kilograms of food in such a way that each Pokémon receives a non-negative integer number of kilograms of food (which may be larger than the capacity of the bowl). The dissatisfaction level of a Pokémon who received

N

kilograms of food and whose bowl has a capacity of

C

kilograms is equal to

\lvert N-C\rvert

.
Find the smallest real number

D

such that, regardless of the capacities of the bowls, Professor Oak can distribute food in a way that the sum of the dissatisfaction levels over all the

100

Pokémon is at most

D

.
Oleksii Masalitin, Ukraine

Problem Statement