Santa 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. Also some had to have both features and 3 dolls were needed having blue eyes and fair hair but were not able to say " I love math". Also santa needed a total of 34 dolls able to say " I love Math" of whom 17 needed to have fair hair. Every doll had at least 1 of sthe features named and there was one combination of features not asked for at all. Several children had asked for all 3 features in the one doll. How many fair-haired, blue -eyed dolls saying "I love math" were needed.
help help help please
13. Here's why:
There are eight possible combinations, which I will refer to as A - H, as follows:
A. Blue, Fair, LoveMath
B. Blue, Fair, NotLoveMath
C. Blue, NotFair, LoveMath
D. Blue, NotFair, NotLoveMath
E. NotBlue, Fair, LoveMath
F. NotBlue, Fair, NotLove Math
G. NotBlue, NotFair, LoveMath
H. NotBlue, NotFair, NotLoveMath
Here are the clues:
1. He knew that he needed 57 in total,
2. that 27 had to have blue eyes
[2a. so 30 do not have blue eyes]
3. and 29 had to have fair hair.
4. His assistant gnome pointed out that some had to have both features
5. and remembered that 3 dolls were needed having blue eyes and fair hair, but which were not able to say 'I Love Math'.
6. he needed a total of 34 dolls able to say ''I Love Math',
7. of whom 17 needed to have fair hair [7a which means that 17 did not have fair hair].
8. "Every doll had at least 1 of the features named";
9. "That there was one combination of features not asked for at all"
10. "Several children had asked for all 3 features in the one doll".
From clue 5 you know B = 3
From clue 8 you know H = 0
From clue 3, A+B+E+F = 29. We already know B = 3, and from clue 7 A+E = 17. So F=9.
From clue 9 you know one of the remaining is 0. Let's guess that C=0 (you can try others, but this seems to work out)
Then from c7a, since C=0 that means G = 17.
From 2a, since E+F+G = 30 and already know F=9 and G=17, so E=4.
From 7, given E=4 then A = 13.
Finally from 2, since A+B+C+D = 30, then D=11.
So:
A = 13 = Blue, Fair, LoveMath
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i don't know!!!!! waaaaaaahh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
mommy? is that you? no!!!! its santa!
To solve this problem, we can use Venn diagrams and a bit of logic. Let's break down the information given and work through it step by step:
1. Santa needed a total of 57 dolls.
2. Santa needed 27 dolls with blue eyes and 29 dolls with fair hair.
3. Some dolls needed to have both blue eyes and fair hair. Specifically, 3 dolls needed to have both features but not be able to say "I love math."
4. Santa needed a total of 34 dolls who can say "I love math," and out of those, 17 dolls needed to have fair hair.
5. Every doll had at least one of the named features (blue eyes, fair hair, or ability to say "I love math").
6. There was one combination of features not asked for at all.
7. Several children had asked for all three features in one doll.
Let's start by drawing a Venn diagram to represent the information given. We'll use three circles to represent the three features: blue eyes, fair hair, and ability to say "I love math."
Now, let's populate the Venn diagram based on the given information:
- The total number of dolls needed is 57. We'll place this number outside the circles.
- 27 dolls needed to have blue eyes. We'll place this number in the circle representing blue eyes.
- 29 dolls needed to have fair hair. We'll place this number in the circle representing fair hair.
- 3 dolls needed to have both blue eyes and fair hair but not be able to say "I love math." We'll place this number in the overlapping area between the circles representing blue eyes and fair hair.
- 34 dolls needed to be able to say "I love math." We'll place this number outside the circle representing this feature.
- 17 dolls needed to have fair hair and be able to say "I love math." We'll place this number in the overlapping area between the circles representing fair hair and ability to say "I love math."
Now, let's analyze the information to determine the remaining numbers:
- The number of dolls with blue eyes only can be calculated by subtracting the number of dolls with both blue eyes and fair hair (3) from the total number of dolls with blue eyes (27 - 3 = 24).
- The number of dolls with fair hair only can be calculated by subtracting the number of dolls with both blue eyes and fair hair (3) from the total number of dolls with fair hair (29 - 3 = 26).
- The number of dolls able to say "I love math" only can be calculated by subtracting the number of dolls with fair hair and being able to say "I love math" (17) from the total number of dolls able to say "I love math" (34 - 17 = 17).
Finally, let's determine the number of fair-haired, blue-eyed dolls saying "I love math":
- Since we have already accounted for the dolls with fair hair and ability to say "I love math" (17), we need to subtract this number from the number of dolls with both blue eyes and fair hair (3) to find the number of fair-haired, blue-eyed dolls saying "I love math" (3 - 17 = -14).
Therefore, based on the given information, it seems there is no possible number of fair-haired, blue-eyed dolls saying "I love math" that satisfies all the conditions provided.
Please note that it's possible there might be errors or logical inconsistencies in the given information. Double-checking the information or seeking clarification might be needed to ensure accuracy.