Girls and Pigs

Problem #97

Tags: puzzle mathematics

Who solved this?

Once upon a time, when I was teaching electronics in the school, I was offering the following task to newcomers in order to check their manner of thinking about problems:

The girls are pasturing pigs at the field. In total they have 106 legs and 336 breasts. How many girls and pigs are there?

Pigs and girls were chosen not just for a joke! The main reason was that the number of breasts for a pig was unknown. So some pupils were telling that "The problem could not be solved", while others were pretending that "there are infinite number of solutions since we have 3 variables and 2 equations".

Of course it is not so! The variables in this problem have some obvious limitations, hence only quite finite amount of solutions could be found - and of them only one looked believable.


Now you are to solve the "extended" version of the task. As before you will be given the number of legs and breasts and your goal is to tell the number of possible solutions.

Input data will have the number of testcases in the first line.
Next lines will contain a pair of values each - the amounts of legs and breasts - the first of them will always be smaller than the second.
Answer should give the amount of solutions for each case.

Example:

input data:
4
6 10
26 136
106 336
200 500

answer:
1 2 3 9

Note: of course we assume that all pigs have the same number of breasts because they are of the same breed - otherwise the problem will become senseless. We also assume this number is even for pigs (as for most mammals), though not limited from the top.


Explanation

For the input data 26 and 136 possible solutions are:

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