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?

(In reply to only one solution? by vj)

504, 810 and 648 are not triangular numbers. Taking successive values of k:

31*32/2 = 496
32*33/2 = 528;  504 would have to be between these; so there's no value of k that works.

39*40/2 = 780
40*41/2 = 820; so there's no 810

35*36/2 = 630
36*37/2 = 666; so there's no 648

Posted by Charlie on 2007-04-23 10:19:00