A, B, C and D are triangular numbers.

A, B and C are always consecutive while D is their sum.

Determine (and explain as best as possible¹) how such sets of values are distributed across the number system.

^1. This can be explained in terms of a single variable expression.

(In reply to computer-aided solution by Charlie)

The first part of your reply is more solid in its data than that which I toyed with when formulating this. 

Dej Mar's comment offers an expression which, was it to my avail, I'd have probably used it to copy down my spreadsheet column.  Then I'd have done as Dej Mar did, exclude those values which were clearly superfluous.  That actually didn't happen.  Having found the second set I wrote a program.  Part of that story is in my solution.

I had set out to explain this event with an expression with just one variable.  You haven't given me that per se.  In your second listing however the equation which begins "ans=..." contains variables a and b, but these are substituted into "ans".

I've taken that into account in the solution as well as offering a related but different approach by Brian Smith.

(Oh! Nearly forgot, I noted the acknowledgement, thanks, but it really was something of insignificance.)

Edited on December 2, 2009, 4:20 am

Posted by brianjn on 2009-12-02 04:17:44