2015 and aliens (and pigeons)
A group of aliens come to visit the world, threatening the mankind. They said they need a group of 2015 people who were born exactly on the same minute in 2015 . If people cannot find the group, then the world will be devastated completely. You, as the brave, want to rescue the world so you made the choice of which country you should search for the best strategy.
The country must surely have the group of people the aliens requested, and should have the least people possible to be easy to control the search.
The data below shows suitable country for the search and its estimated population in 2015:
- China - 1,372,560,000
- United States - 322,001,000
- Japan - 126,832,000
- Thailand - 65,104,000
- Australia - 23,924,700
Which of the following is the best country that fits the given condition?
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1 solution
This problem can be solved using Pigeonhole Principle k = ⌊ m n − 1 ⌋ + 1
There are 6 0 minutes in an hour.
There are 2 4 hours in a day.
There are 3 6 5 days in 2015.
The total of different times people were born is 6 0 × 2 4 × 3 6 5 = 5 2 5 , 6 0 0 .
We need to be sure that 2015 people will share the same minute of birth this year.
From the above, k = 2 0 1 5 and m = 5 2 5 , 6 0 0 .
2 0 1 5 = ⌊ 5 2 5 , 6 0 0 n − 1 ⌋ + 1 2 0 1 4 = ⌊ 5 2 5 , 6 0 0 n − 1 ⌋ 2 0 1 4 = 5 2 5 , 6 0 0 n − 1 2 0 1 4 × 5 2 5 , 6 0 0 = n − 1 1 , 0 5 8 , 5 8 8 , 4 0 0 = n − 1 n = 1 , 0 5 8 , 5 8 8 , 4 0 1
We need at least 1 , 0 5 8 , 5 8 8 , 4 0 1 people to be sure.
Therefore, the only capable country for the situation is C h i n a .