Question

Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least:

• A. 5
• B. 103
• C. 6
• D. Cannot be determined

Hint:

In distribution problems, apply the pigeonhole principle: $\lceil \frac{\text{total items}}{\text{categories}} \rceil$ gives the minimum repetition count.

Answer 1

The Correct Option is C

Possible number of oranges in a box: from 120 to 144 inclusive. Number of possible values = $144 - 120 + 1 = 25$.
By pigeonhole principle: If 128 boxes are distributed among 25 possible counts, then at least $\lceil \frac{128}{25} \rceil = 6$ boxes must have the same number.