DD/MM/YYYY and MM/DD/YYYY

Question

• A father and his son is from a country where the date format used is DD/MM/YYYY.
• In 2022, they visited a country for a day where the date format used is MM/DD/YYYY.

Predict the birth dates of the son and his father along with the date of their visit.

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Birth date of son (DD/MM/YYYY)

• When his birth date is written according to the date format of his country, it is not one of the possible dates according to the country he visited.
• DD and MM are prime numbers.
• YYYY is a combination of all the four digits used in DD and MM.
• His age as on the day of his visit was not a prime number.

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Birth date of father (DD/MM/YYYY)

• When his birth date is written according to the date format of his country, it is not one of the possible dates according to the country he visited.
• DD is a prime number while MM is equal to the age of his son as on the day of their visit.
• YYYY is a combination of all the four digits used in DD and MM.
• His age as on the day of his visit was a prime number.

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Date of visit (MM/DD/2022)

• The year 2022 is a combination of all the four digits used in MM and DD.

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Answer 1

The dates are (all dd/mm/yy format):

Date of visit: 22/02/2022
Date of son's birth: 13/02/2013
Date of father's birth: 19/09/1990

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Date of visit:

The only possible date it can be is 22/02/2022 with the combination of numbers available.

The son:

Starting with the fact the reverse date cannot exist, the day must be more than 12. So with the prime numbers, the days can be 13, 17, 19, 23, 29 or 31 and the month can be 02, 03, 05, 07 or 11.

The son must be born after 2000, as no combination can make a high 19?? date. With that in mind, the month has to be 02, and the day has to be 13, 17 or 19.

So what year? Well we just have to look at the potential ages: 9 for 2013, 5 for 2017, 3 for 2019, and as it is not prime, the son was born on 13/02/2013

The father:

Once again, the day is above 12 and prime, so 13, 17, 19, 23, 29 or 31. We know that the month is 09 for his son's age on the day of the visit.

The father must be born in 19??, so to make a valid year with 09, the day must be one of 13, 17 and 19 - with potential years being 1930, 1970 and 1990.

Looking at the potential ages, 91, 51 and 31, only 31 is prime, so the father was born on 19/09/1990