Question 82
Each pupil in the Netherlands is given 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 each person has been given.
Any pupil for whom the sum of the numbers on their cards is at most $1000$ can distribute their cards over $100$ boxes such that the sum of the cards in each box is at most $c$.
Any pupil for whom the sum of the numbers on their cards is at most $1000$ can distribute their cards over $100$ boxes such that the sum of the cards in each box is at most $c$.