Sorting cars in line

There are 25 25 cars stored in a straight line-shaped garage and are numbered 25 , 24 , 23 , . . . , 3 , 2 , 1 25, 24, 23, ..., 3, 2, 1 in that order. You want to rearrange them in the reverse order 1 , 2 , 3 , , 23 , 24 , 25 1, 2, 3, \cdots, 23, 24, 25 . You are allowed to switch only any two adjacent cars at a time. To switch two adjacent cars, you need 2 2 drivers to do so. Assume that there are 10 10 drivers and the average time required to switch two adjacent cars is 1 1 minute. What is the minimum time required to do this job?

* Assume that there is enough space for the 10 drivers to drive and move cars. *


The answer is 60.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Ossama Ismail
Oct 19, 2020

This can be done by using the odd-even sorting technique. If you are going to rearrange the cars using two drivers, you need to make 25 C 2 ^{25}C_2 switching between two cars. When using 10 drivers the number of switching, the total time required to complete the job = 25 C 2 2 = 60 \large {= \frac{^{25}C_2 }{2} = 60} minutes }.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...