# Modified Census Taker Problem

The census taker has arrived at yet another house, and is greeted by a busy housewife. This woman poses a new riddle: "2 of my girls have red hair, the rest are brunettes. All 8 of my boys have black hair. What percentage of my children are girls?" she asks. The census taker is stumped, and instead decides to help her put the dozen popsicles she bought for her kids in the fridge, and watches as the mother scolds a child for not wanting to share his toys. "All of my children are so greedy she says". The census taker decides to skip this house, since he isn't feeling like unnesesarily hard riddles. Did the census taker give up too easily? If so, what was the answer to the mother's question?

I made the problem myself, so do tell me what you think about it and how I could improve it.

• When the census taker got back to HQ and told his boss the story, his boss said, "You're fired!" Fortunately, census taking is only a temp job. Nov 19, 2014 at 3:58

The number of girls she has is:

4

Meaning the percentage of girls is:

4 / 12 or one-third or 33.333... %

Reasoning:

She put a dozen popsicles in the fridge. She has at least 2+8=10 kids, so 12 is the only number of kids to evenly divide the popsicles so each kid has at least 1 - and the busy housewife knows if there are extras or anybody has to share, the house will be full of strife.

• +1 for phrasing it as "the house will be full of strife." Nov 19, 2014 at 3:25
• I understand that this is the intended answer but I am bothered by the assumption that the mother buying 12 popsicles means that she has 12 kids. What if she has 16 kids and there were 4 left over from the last box so she rushed out to buy more? There is a lateral-thinking tag after all. May 11, 2015 at 19:09
• @EngineerToast Fortunately this wasn't a hot dog/hot dog bun question... May 11, 2015 at 19:23

He could observe that one dozen popsicles were bought for the kids, and the mother said they were greedy, so we can assume she wouldn't have wanted to deal with either a shortage or surplus when handing them out. So,

there can be no more than 12 kids, and there are almost certainly exactly 12 kids.

10 are either redheaded girls or black-haired boys. "The rest" are brunette girls, the term implying

more than one brunette, reinforcing the previous spoiler.

Therefore we can say that there are

2 brunette girls,

and therefore the percentage of girls among the children in the household is

4/12 = 1/3 = 33.33%