Difference between revisions of "2024 AMC 10B Problems/Problem 4"
m (Protected "2024 AMC 10B Problems/Problem 4" ([Edit=Allow only administrators] (expires 04:59, 14 November 2024 (UTC)) [Move=Allow only administrators] (expires 04:59, 14 November 2024 (UTC)))) |
|||
| Line 1: | Line 1: | ||
| + | {{duplicate|[[2024 AMC 10B Problems/Problem 2|2024 AMC 10B #4]] and [[2024 AMC 12B Problems/Problem 2|2024 AMC 12B #4]]}} | ||
| + | ==Problem== | ||
| + | Balls numbered 1, 2, 3, ... are deposited in 5 bins, labeled A, B, C, D, 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 22, 23, ..., 28 are deposited in bin B at step 7 of this process.) In which bin is ball 2024 deposited? | ||
| + | |||
| + | <math>\textbf{(A) } A \qquad\textbf{(B) } B \qquad\textbf{(C) } C \qquad\textbf{(D) } D \qquad\textbf{(E) } E</math> | ||
| + | |||
| + | ==Solution 1== | ||
| + | |||
| + | Ball D, 63*64/2=2016. | ||
| + | |||
| + | ==See also== | ||
| + | {{AMC10 box|year=2024|ab=B|num-b=3|num-a=5}} | ||
| + | {{AMC12 box|year=2024|ab=B|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
Revision as of 00:33, 14 November 2024
- The following problem is from both the 2024 AMC 10B #4 and 2024 AMC 12B #4, so both problems redirect to this page.
Problem
Balls numbered 1, 2, 3, ... are deposited in 5 bins, labeled A, B, C, D, 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 22, 23, ..., 28 are deposited in bin B at step 7 of this process.) In which bin is ball 2024 deposited?
Solution 1
Ball D, 63*64/2=2016.
See also
| 2024 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2024 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
