### Brain Teasers

# Santa's Dilemma

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?

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

### Answer

13 dolls were neededHide Answer Show Answer

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## Comments

Well, at least this one had nothing to do with kebabs...

Okay, so how did you get there? I got lost trying to figure out what equation to use.

Meh...

I don't know how you got 13 but I kept geting 21 no matter how hard I tried. can someone please explain the answer

I will reserve judgement on this teaser until someone can either enlighten or correct me.

I have the following:

1 that says only Mama, 16 that say Mama and have Blue eyes but not fair hair; 9 that say Mama and have fair hair but not blue eyes and 8 that have all 3 features.

9 have Fair hair only and the only combination missing is Blue eyes only without Fair hair and doesn't say Mama.

According to my Venn diagram this satisfies all of the described conditions and my answer is 8?

I have the following:

1 that says only Mama, 16 that say Mama and have Blue eyes but not fair hair; 9 that say Mama and have fair hair but not blue eyes and 8 that have all 3 features.

9 have Fair hair only and the only combination missing is Blue eyes only without Fair hair and doesn't say Mama.

According to my Venn diagram this satisfies all of the described conditions and my answer is 8?

I left out the 3 given that have blue eyes and fair hair but do not say Mama. This totals 57. ?? What am I missing?

How to do?

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