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Counting Quadruplets II (Posted on 2010-09-21) Difficulty: 3 of 5
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?

No Solution Yet Submitted by K Sengupta    
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precedence / solution | Comment 1 of 2

If one assumes the normal operator precedence rules (i.e. when not overrides by parentheses) for such expressions, e.g. multiplications and divisions before additions and subtractions, ----- then:

(a) A * B + C * D is read as (A*B) + (C*D).  There are 3254 quadruplets evaluating 300 or greater.

(b) A * B - C * D is read as (A*B) - (C*D).  There are obviously no evaluations greater than 100, since (C*D) will always be greater than (A*B) unless ABCD are all the same in which case also an evaluation of zero is less than 100.

If some different interpretation was the intent, the text  expression should be fully parenthesized. 

  Posted by ed bottemiller on 2010-09-21 14:05:30
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