Examkin

Question

Difficulty: MediumOrder and Ranking

In a single row of books on a library shelf, an Encyclopedia is 28th28^{\text{th}} from the left end and a Dictionary is 35th35^{\text{th}} from the right end. If there are exactly 12 books placed strictly between them, what is the minimum possible total number of books in this row?

Answer: 49

Answer

The minimum possible total number of books is 49.
The minimum total is found using the overlapping queue formula: L+R−M−2L + R - M - 2. Substituting the given values yields 28+35−12−2=4928 + 35 - 12 - 2 = 49.

Step-by-Step Solution

1
Identify the queue configuration for the minimum capacity.
The minimum possible number of books occurs in an overlapping scenario.
In an overlapping scenario, the item counted from the right (Dictionary) is placed to the left of the item counted from the left (Encyclopedia), yielding the smallest overall total length.
2
Apply the minimum capacity formula.
Total=L+R−M−2\text{Total} = L + R - M - 2
We add the rank from the left (LL) and the rank from the right (RR), then subtract the number of items strictly between them (MM) and the 2 reference items to correct for double-counting.
3
Substitute the given values and calculate the final count.
Total=28+35−12−2=49\text{Total} = 28 + 35 - 12 - 2 = 49
This yields the exact minimum count of books on the shelf.

Key Concept

Overlapping Minimum Capacity in Ordering and Ranking
Estimated Time:1m 0s
Rate this question

Topics

Order and Ranking

More questions from this topic