UGC NET CSE | June 2005 | Part 2 | Question: 5

Question

Minimum number of individual shoes to be picked up from a dark room ( containing $10$ pair of shoes) if we have to get atleast one proper pair :

• A. $2$
• B. $20$
• C. $11$
• D. None of these

Answer 1

Answer is option c;

This follows from pigeon hole principle

In worst case,you take only 1 shoe from every pair.

Now if you take a shoe from the remaining 10 shoes

you will definitely have a pair.

Ps:

Thing is we try to avoid getting pair of shoes as much as we can.when we pick 10 shoes (1 from each pair),we can't avoid getting a pair further.Hence any shoe taken now will form a pair

Answer 2

C. 11 ..

There are 10 pair of shoes. A single proper matching pair can be found out only when we pick the 11th shoe because till 10th shoe we cannot be very sure that we will get the right pair....

But the 11th shoe that we take will definitely let us match the right pair surely. ...