Tom, Dick and Harry were searching for 3-digit triangular numbers (numbers of the form k*(k+1)/2) that are themselves each the product of three different triangular numbers greater than 1 (so 1*3*15 = 45 doesn't count, nor does 3*10*10 = 300 because of the duplicated 10).

Each of them found a different triangular number. One of the triangular factors is found only in Harry's solution. Another of the triangular factors is found only in Tom's solution.

What are the three triangular factors making up Dick's solution?

I'm afraid I'm losing something in the puzzle.

I have several possibilities... As far as I can understand from what I read, i got upon a lot of triangular numbers that could fit Harry's, Tom's and, subsequentally, Dick's solution...

For instance, 180 (3*6*10), 378 (3*6*15), 504 (3*6*28), ..., are all triangular numbers with factors that are exclusive (10, 15, 28, ...). Dick's solution could be 648 (3*6*36), 810 (3*6*45), 990 (3*6*55), amongst many others... and without even leaving the 3*6 base...

What's on then?

Posted by vj on 2007-04-23 09:33:13