MHB Johns Born Same Day: 24M Humans, 4 Letters

  • Thread starter Thread starter mathworker
  • Start date Start date
  • Tags Tags
    Hole Proof
AI Thread Summary
With only 24 million humans and a name limit of one million per name, the Pigeonhole Principle indicates that at least two individuals named John must share the same birth date. Given that there are only 365 days in a year, this creates a scenario where the distribution of births among a limited number of names leads to overlaps. The four-letter name 'John' restricts the possibilities further, making it statistically inevitable. The discussion emphasizes the implications of population limits and naming conventions over a historical timeline of 2739 years. Thus, it is mathematically proven that at least two people named John must have been born on the same day.
mathworker
Messages
110
Reaction score
0
Prove that least two humans named John should have born on same day(means with same D.O.B) if world has only 24 million humans and their alphabet chart contain just 4 letter 'J','H','O' and 'N' and there can't be more than one million humans of same name and world started just 2739 years ago.

source:Pigeon hole principle
 
Mathematics news on Phys.org
mathworker said:
Prove that least two humans named John should have born on same day(means with same D.O.B) if world has only 24 million humans and their alphabet chart contain just 4 letter 'J','H','O' and 'N' and there can't be more than one million humans of same name and world started just 2739 years ago.

source:Pigeon hole principle
let x=numbers of humans with the same name

x=$\dfrac {24\times 1000000}{4!}=1000000$

$\dfrac {1000000}{365}=2739.726027397$(suppose world started just 2739 years ago)

$\dfrac {2739.726027397}{2739}>1 $

$\therefore$ at least two humans named John should have born on same day
 
Last edited:
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

Similar threads

2
Replies
67
Views
14K
Replies
129
Views
20K
Replies
17
Views
8K
Replies
42
Views
7K
Replies
1
Views
3K
Replies
8
Views
5K
Replies
1
Views
3K
Back
Top