Charmaine has written down three 3-digit positive integers which between them contains exactly 9 distinct digits.

Among these three positive integers:

• There is at least one that is divisible by 2.
• There is at least one that is divisible by 3.
• There is at least one that is divisible by 4.
• There is at least one that is divisible by 5.
• There is at least one that is divisible by 6.
• There is at least one that is divisible by 7.
• There is at least one that is divisible by 8.
• There is at least one that is divisible by 9.

In addition, it is known that all the three positive integers are divisible by 11.

What are the three 3-digit integers posited by Charmaine?

Note: Adapted from Enigma # 1776 which appeared in 'New Scientist' in 2013.

(In reply to re: Answer by Steve Herman)

Oof, I am a bit embarrassed about such a large omission.  Everything in my solution up through figuring 792 is a multiple of 72 was purely a transcript of mental math.  

Posted by Brian Smith on 2023-07-04 10:16:15