Question #102009
Three football players had the following conversation.
Messi: I just realized that our uniform numbers are all 2-digit primes.
Ronaldo: And the sum of your two uniform numbers is the date of my birthday
earlier this month.
Neymar: That's funny. The sum of your two uniform numbers is the date of my
birthday later this month.
Messi: And the sum of your two uniform numbers is today's date.
What number does Ronaldo wear?
Messi: I just realized that our uniform numbers are all 2-digit primes.
Ronaldo: And the sum of your two uniform numbers is the date of my birthday
earlier this month.
Neymar: That's funny. The sum of your two uniform numbers is the date of my
birthday later this month.
Messi: And the sum of your two uniform numbers is today's date.
What number does Ronaldo wear?
Expert's answer
The maximum amount of days any given month can have is 31, and the smallest two digit primes are 11, 13, and 17. There are a few different sums that can be deduced from the following numbers, which are 24, 30, and 28, all of which represent the three days. Therefore, since Ronaldo says that the other two people's uniform numbers are earlier, so that means Neymar's and Messi's numbers must add up to 24. Similarly, Neymar says that the other two people's uniform numbers are later, so the sum must add up to 30. This leaves 28 as today's date. From this, So, Ronaldo was referring to the uniform wearers 11 and 13, telling us that his number is 17.
