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# win fri\$2

chennai
solve this riddle

Father Christmas had a problem. He was making up a batch of dolls but could not remember exactly how many of each kind he needed. He knew that he needed 57 in total, that 27 had to have blue eyes, and 29 had to have fair hair. His assistant gnome pointed out that some had to have both features and remembered that 3 dolls were needed having blue eyes and fair hair, but which were not able to say 'Mama'. This prompted the old man to remember that he needed a total of 34 dolls able to say 'Mama', of whom 17 needed to have fair hair. The assistant was going around in circles juggling all this information but couldn't work it out. He pressed for any other bits of information that Father Christmas just might be able to manage, no matter how trivial. The only items he got were: "Every doll had at least 1 of the features named"; "That there was one combination of features not asked for at all" and "Several children had asked for all 3 features in the one doll". That was enough!

How many fair-haired, blue-eyed dolls saying 'Mama' were needed

the winner gets fri\$2
omeration
chennai
no omeration you are wrong
rvec
i know it is less than 17. But how many less.....
edit: is it 17?
ocalhoun
two guesses:
1) several.
2) 54
djared90
The answer is that 13 dolls that had all three features were needed.

Here I will show the steps as to how I got this answer:
1. I took the information: "27 had to have blue eyes, 29 had to have fair hair, and 3 dolls needed to have blue eyes and fair hair, and came up with:
Only blue eyes: 27 - 3 = 24
Only fair hair: 29 - 3 = 26
Only blue eyes and fair hair: 3

2. "total of 34 dolls able to say 'Mama,' of whom 17 needed fair hair"
Only blue eyes: 24
Only fair hair: 26 - 17 = 9
Only say mama: 34 - 17 = 17
Only blue eyes and fair hair: 3
Only say mama and fair hair: 17

3. "one combination of features not asked for at all"
Only blue eyes: 24
Only fair hair: 9
Only say mama: 17
Only blue eyes and fair hair: 3
Only say mama and fair hair: 17
Only say mama and blue eyes: 0

4. There can only be three that have only blue eyes and fair hair, but with the ones that say mama and have fair hair, they can also have blue eyes.

As it turns out right now, I have marked a total of 70, but there are only 57 in total. So, there are 13 too many.

I can add 13 of the dolls that already have fair hair and say mama to also have blue eyes, creating the following:
Only blue eyes: 24 - 13 = 11
Only fair hair: 9
Only say mama: 17
Only fair hair and blue eyes: 3
Only say mama and fair hair: 17 - 13 = 4
Only say mama and blue eyes: 0
All three: 13

Which satisfies all stated conditions, so the answer is 13.
chennai
you are right djared90.i will send u the prize money
ocalhoun
There was a whole lotta "Only"s that spontainiously generated from nowhere...