Question 146
Each student of a class has a finite number of cards. Each card has a number on it from the interval $[0,1]$. Find the smallest possible constant $c \gt 0$ such that the following holds, independently of the distribution of the cards to the students:
Each student who has a total sum of numbers less than 1000 can share the cards into 100 boxes such that the sum of the cards in each box is at most $c$.
Each student who has a total sum of numbers less than 1000 can share the cards into 100 boxes such that the sum of the cards in each box is at most $c$.