Problem:
Balls numbered are deposited in 5 bins, labeled , and E , using the following procedure. Ball 1 is deposited in bin A, and balls 2 and 3 are deposited in bin B . The next 3 balls are deposited in bin C , the next 4 in bin D , and so on, cycling back to bin A after balls are deposited in bin E. (For example, balls numbered are deposited in bin B at step 7 of this process.) In which bin is ball 2024 deposited?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
After steps, a total of balls have been deposited. In particular, after step , a total of balls have been deposited. The next batch of 64 balls will include ball 2024. Because 64 has remainder 4 when divided by 5, ball 2024 is deposited in bin .
The problems on this page are the property of the MAA's American Mathematics Competitions