Question 92
Every pupil in the Netherlands receives a finite number of cards. On each card there is a real number in the interval $[0,1]$. (The numbers on different cards do not have to be different.) Find the smallest real number $c\gt 0$ for which the following holds, independent of the numbers on the cards that everyone has received.
Every pupil for whom the sum of the numbers on the cards is at most 1000 can distribute the cards over 100 boxes such that the sum of the cards in each box is at most $c$.
Every pupil for whom the sum of the numbers on the cards is at most 1000 can distribute the cards over 100 boxes such that the sum of the cards in each box is at most $c$.