MathDB

In an exotic country, the National Bank issues coins that can take any value in the interval

[0, 1]

. Find the smallest constant

c > 0

such that the following holds, no matter the situation in that country:
Any citizen of the exotic country that has a finite number of coins, with a total value of no more than

1000

, can split those coins into

100

boxes, such that the total value inside each box is at most

c

Problem Statement