Jeez michael, i'm sorry  but i am not going to go 
through all of your code. 

I do have a suggestion for you, without looking at 
the code.

As you know. php has flexible variables. I mean, if 
you say $a=1 then $a is an integer, if you say 
$b='i' then $b is a string.
Very easy to make code quickly, but for the larger 
scripts it can be a pit trap.

I think that while you intended the variables to be 
numbers, they somehow turned into strings. Maybe 
you added a (empty) string somewhere ($a .='').

Several ways to deal with it.
First have a look at what is in the variable:

echo '<hr>string "a" is ['.$a.']';
i always add something around the string to see 
spaces.

Another thing you can try is to force the value 
into an integer.
I think something like

$c= intval($a) - intval ($b);

but have  a look around the manual to be sure.

hth, let me know at my own email if it helped?

Chris


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