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Consecutive Triangles (Posted on 2009-11-29) Difficulty: 4 of 5
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.

See The Solution Submitted by brianjn    
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an observation | Comment 4 of 8 |
The ordinal number x of a triangular number Tx which is the sum of three consecutive triangular numbers can be found where
x = SQRT(3n2 + 9n + 33/4) - (1/2)
such that x is an integer and n is the ordinal number Tn of the first of the three consecutive triangular numbers.
  Posted by Dej Mar on 2009-11-30 04:40:05
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