# Puzzle | Can 2 persons be with same number of hairs on their heads?

One day Ram and Shyam were searching Google for finding what is the maximum number of hairs on the human head. They found that it is 2, 00, 000. Then Shyam thought a while and suddenly made a statement that there are at least two Bengaluru citizens who have got the exact same number of hairs on their heads. Both of them knew the fact that the population of Bengaluru is 1.23 crores.

But Ram was still thinking whether Shyam’s statement is correct or not.

**Is Shyam’s statement 100% correct or we need more information to deduce the truth of the statement?**

**Answer:**

Shyam’s statement is 100% correct!

**Solution:**

Assume you are sorting the citizens according to the number of hairs on their heads. Then, you can imagine virtual bins with these number of hairs on their heads:

0, 1, 2, …., 2, 00, 000 (for a total of 2, 00, 001 bins)

But there are 1.23 crores of them and at least two should be in the same bin.

This problem and solution are based on ‘Pigeonhole principle‘.

There is nothing related to probability in this and Shyam’s statement is 100% correct!

In fact if we assume the total number of people in the city with at most 10, 000 hairs are 23, 00, 000, there will be at least two persons who have same number of hairs, the number being greater than 10, 000 hairs, on their heads. This is because, after taking away 23, 00, 000 people from 1.23 crore, we still have 1 crore people and 1, 90, 000 bins only (namely 10, 001, 10, 002, …, 2, 00, 000)!

## Recommended Posts:

- Puzzle | Heads or Tails
- Puzzle 43 | Muddy Heads
- Puzzle | 1000 light bulbs switched on/off by 1000 persons passing by
- Expected number of coin flips to get two heads in a row?
- Expected Number of Trials to get N Consecutive Heads
- Puzzle | Number of Sheets to be turned so that Prime Number has a Vowel on the other side
- Time taken by two persons to meet on a circular track
- Puzzle 69 |The Number Game
- Puzzle 78 | The lost bus Number
- Puzzle | (Something for the marmalade , Number Game)
- Puzzle | Find Number of matches
- Puzzle | Guess the total number of coins
- Puzzle 71 | Correct Number to save life
- Puzzle | Maximum number of Kings on Chessboard without under check
- Puzzle | Minimum number steps to weigh 1 kg rice with 1gm weight
- Minimum number of moves required to solve a Jigsaw Assembly Puzzle
- Puzzle 51| Cheryl’s Birthday Puzzle and Solution
- Puzzle 85 | Chain Link Puzzle
- Puzzle 15 | (Camel and Banana Puzzle)
- Puzzle 81 | 100 people in a circle with gun puzzle

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.