J. Weldon Wolfingham, Jr. will marry one of these women: Adrianna, Bianca, and Claire.
Some clues are furnished hereunder as follows:
1. Of Adrianna and Bianca:
• (a) Either they are both have blue eyes, or neither has blue eyes.
• (b) One has red hair and the other does not.
2. Of Adrianna and Claire:
• (a) Either they both have red hair, or neither has red hair.
• (b) One is 5'11" and the other is not.
3. Of Bianca and Claire:
• (a) One has blue eyes and the other does not.
• (b) One is 5'11" and the other is not.
4. Of the three characteristics - blue eyes, red hair and 5'11":
• (a) If any of the three women has exactly two of the three characteristics, Mr. Wolfingham will marry the one with the least number of characteristics.
• (b) If any of the three women has exactly one of the three characteristics, Mr. Wolfingham will marry the one with the greatest number of characteristics.
Who will Mr. Wolfingham marry?
Let 1 = yes and 0 = No.
For A|B|C:
Blue eyes (clues 1 & 3): 110 or 001
Red hair (clues 1 & 2): 101 or 010
5'11" (clues 2 & 3): 110 or 011
This provides 2^3 combinations (with summation):
1.
A B C
1 1 0
1 0 1
1 1 0
3 2 1
2.
A B C
1 1 0
1 0 1
0 0 1
2 1 2
3.
A B C
1 1 0
0 1 0
0 0 1
1 2 1
4.
A B C
0 0 1
1 0 1
1 1 0
2 1 2
5.
A B C
0 0 1
0 1 0
1 1 0
1 2 1
6.
A B C
0 0 1
0 1 0
0 0 1
0 1 2
7.
A B C
0 0 1
1 0 1
0 0 1
1 0 3
8
A B C
0 0 1
1 0 1
0 0 1
1 0 3
Combinations 1 thru 6 can be eliminated since they exhibit women having both 1 and 2 characteristics, thus contradicting rules 4a and 4b. That leaves combinations 7 and 8.
Combination 7 shows Adrianna with 2 characteristics, with Claire having the least (4a).
Combination 8 shows Adriana with 1 characteristic with Claire having the most (4b).
Therefore, Claire is the fiancé.
Bianca either exhibits all three characteristics, or she exhibits none.
Edited on March 1, 2023, 8:52 pm
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Posted by hoodat
on 2023-03-01 20:45:37 |
Solution (Excel)
