First of all, ABC have to form a triangle, so we know
that
C<A+B
This shows us that
C-B<A
Also, because of the ordering criteria, (C>B, B>A) we know that
A<B
If we put this information together we see that
C-B<A<B
This means that our (inclusive) upper bound for A is B-1 and
that our (exclusive) lower bound for A is C-B.
Given this information, our range for A is
(B-1)-(C-B)=2B-1-C *
Let's look at a real number example:
let C=25 and B=18
A can have a value no greater that 17 (B-1=18-1)
and no less than 8=C-B+1=28-18+1 (remember that if A=C-B we would get a straight
line)
So A can be 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.
That is, there are 17-7=10 values that A could be.
Take a look at a
visual representation of
this problem.
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