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Santa's Sack of Gifts

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Santa's Sack of Gifts

This year Santa was so busy overseeing the business of creating toys that he never got around to managing his lists of good children and bad children.

So he decided to give gifts to the first two out of every three boys, and then a lump of coal to the third.

Similarly, he decided to give a present to the first four out of every five girls, and a lump of coal to the fifth.

Finally, he gave presents to the first three out of every four parents, and coal to the fourth.

The first two families he visited had three boys, two girls, and two parents. The next family he visited had one boy and two girls, and one parent. Then he visited two families which each had one boy, one girl, and two parents, and then he visited a family with five boys, three girls, and one parent.

If he did not give any lumps of coal at the next home, what is the largest possible number of people in that family?

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Problem by Mr. Twitchell

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