# Twelve friends born on month ends

Twelve close friends were born on the last dates of their respective birth months. Fascinatingly, their birth months are different.

On 30th June 2023, all twelve of them had gathered for the birthday party of one of them who turned 30.

On that particular day, this was the statistic:

Age Number of friends
28 1
29 2
30 7
31 2

One of them noticed something and said:

On the day we all gather for my birthday party, our ages will be the same as our respective birth dates!

On which day (Date, Month and Year) will that unique birthday party be?

On the date of the party, the ages will be either

28, 4x30, 7x31, or
29, 4x30, 7x31.

Comparing these against the statistics from June 30th, we'll need

• exactly 5 more months with 31 days, each transforming a 30 into a 31
• exactly 2 more months with 30 days, each transforming a 29 into a 30
• possibly 1 more month with 29 days.

Counting ahead with July (31), August (31), September(30), October (31), November (30), December (31) and January (31), we have reached the exact requirements.

So the party is on

January 31st, 2024

because although that year is indeed a leap year, the year 29 years earlier isn't, so the person born in February cannot have been born on the 29th.