Determine the four smallest but different three digit positive decimal integers commencing with the same digit, such that their sum is divisible by precisely three of the said numbers.

What are the five smallest but different four digit positive decimal integers commencing with the same digit, such that their sum is divisible by precisely four of the said numbers?

While I would not like to respond to the comments received so far at this early stage, I wish  to point out that without the "smallest" restriction, there is at least one other set  (1080, 1260, 1512, 1818, 1890) that satisfies  conditions of Part -2, since:

1080 + 1260 + 1512 + 1818 + 1890 = 7560 and 7560 is divisible by each of 1080, 1260, 1512 and 1890 ( with the exception of 1818)..

I may add that this problem also possesses an analytic solution and look forward to comments from members in that direction.

 

 

Edited on September 25, 2006, 11:49 pm

Edited on September 26, 2006, 4:39 am

Posted by K Sengupta on 2006-09-25 23:48:36