Each of A, B, C and D is a positive integer with the proviso that A ≤ B ≤ C ≤ D ≤ 20
Determine the total number of quadruplets (A, B, C, D) such that: A*B + C*D > 300.
What is the total number of quadruplets (A, B, C, D) such that: A*B  C*D > 100?
FOR a = 1 TO 20
FOR b = a TO 20
FOR c = b TO 20
FOR d = c TO 20
IF a * b + c * d > 300 THEN gt300 = gt300 + 1
IF a * b  c * d > 100 THEN gt100 = gt100 + 1
IF c * d  a * b > 100 THEN rgt100 = rgt100 + 1
ct = ct + 1
NEXT
NEXT
NEXT
NEXT
PRINT gt300, gt100, rgt100, ct
shows
3254 0 6347 8855
That is, of the 8855 quadruplets meeting the ordering criteria, 3254 have A*B + C*D > 300, but none have A*B  C*D > 100. If the latter were reversed, however, there'd be 6347 with C*D  A*B > 100.

Posted by Charlie
on 20100921 17:36:38 