The Apple Problem

There is a box full of apples, it has more than 80 but less than 85 apples in the box, some of the apples are red and the others are green, if you divide all the red apples in the box into groups of 4, 1 is left over.

After a while, one person came, took away more than 15 green apples and then ran away.

Then, another person came and checked the box, he wanted to match 1 red apple and 1 green apple as a pair, after he matched all the possible pairs, he finds out there are less than 13 red apples that can't be matched as a pair.

At this point, if he switches some of the red apples, the same number as \(\frac{1}{4}\) of stolen green apples, to green, then only 2 red apples can't be matched as a pair.

If there are originally at least 37 red apples in the box, what is the original number of apples in the box?


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