Guess my birthday

Number Theory Level pending

Adrian and Evan are guessing each other's birthdays during an icebreaker session. Adrian says, “In the DD/MM/YYYY format¹, the sum of the digits of DD is equal to MM. The units and tens digits of DD are each prime numbers. DD and MM are both prime as well.”

Evan took a while to guess Adrian’s birthday and found that only one combination of DD and MM satisfies all the criteria.

Find the sum of all the digits used to make up DD and MM.

¹ For example, 17/08/1964 means 17 August 1964.

The answer is 10.

2 solutions

Saya Suka
Apr 4, 2021

"The units and tens digits of DD are each prime numbers"
==> then the tens must be 2, and DD must either be 23 or 29
==> but 9 in 29 isn't prime, so the units digit of DD part of this rule is violated
==> DD must be 23 and MM = 2 + 3 = 05

Answer = 2 + 3 + 0 + 5 = 10

Philip Lee
Mar 8, 2018

It is known that all prime numbers are odd with the exception of $2$ .

Since the digits of DD add up to MM, it can be concluded that one of the digits in DD is $2$ .

Hence, DD can only be the set of numbers $\{02, 12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29\}$ ( $32$ onwards can be ignored as $31$ is the maximum in a month). From this set of numbers, only $23$ and $29$ are prime. However, $9$ in the units digit of $29$ is not prime so it is excluded.

We check that adding the digits of $23$ gives us $5$ , which is also prime. Hence, we can conclude $23$ May is the answer and so the sum will be $2+3+5=10$ .

Guess my birthday

The answer is 10.

2 solutions

0 pending reports