Question

How many boxes have at least one sack containing 9 coins?

• A. 3
• B. 4
• C. 5
• D. 8

Answer 1

The Correct Option is C

To determine the number of boxes with at least one sack containing 9 coins, we need to analyze the information given in the problem. We have two tables with 3x3 arrangements, totaling 9 boxes. Each box contains 3 sacks. Our goal is to identify how many of these boxes have at least one sack with exactly 9 coins. According to the conditions provided:

1. The median for some boxes is given. For any box where the median is 9, there must be at least one sack with 9 coins. These boxes need to be identified from Table 1.
2. In Table 2, if a box has the conditions specified with "**" markers, it implies two or more of the conditions are satisfied, including condition (iii), which confirms the presence of a sack with 9 coins.

By examining these points against the data:

• Boxes with median 9 from Table 1 automatically qualify.
• Boxes marked with ** in Table 2 should also be included in the count, as they satisfy two or more conditions, including the maximum of 9 coins in at least one sack.

Thus, logically combining these deductions, there are 5 boxes that meet the criteria of having at least one sack with 9 coins.