Logical Reasoning: How Many Points Did They Get (PuzzleUp)

逻辑推理：拿了多少分(PuzzleUp) 苏剑林 · 2009-08-06 · Mathematics logic reasoning

A, B, C, D four people answered 10 yes/no questions, getting one point for each correct answer. The four people's answers, along with A, B, and C's scores, are shown in the figure. What is D's score? (Additional note: wrong answers are not penalized.)

Actually, this puzzle has already been made quite easy, so I'd still recommend everyone give it a try.

If you really don't feel like thinking it through, you can just look at the answer (not recommended). more

A got two questions wrong, and C got 3 questions wrong, which means A and C's answers must agree on at least (10-2-3=5) questions. Looking at the data, we find that A and C's listed answers happen to match on exactly 5 questions, so these five questions' answers must be the correct ones.

Since we now know the correct answers to 5 questions, we can determine that among B's 4 correct answers, 3 have already been pinned down.

Now we can assume that one of B's remaining answers is correct, in which case the rest must be wrong; then, comparing against A and C's data, we check whether this yields 8 and 7 correct answers respectively. Upon checking, it turns out B's first question is indeed correct. However, other possibilities can also arise — B isn't necessarily correct on the first question. After final verification, there turn out to be three possible answer sets in total:
**Y N Y Y Y N Y Y Y N
N N N Y Y N Y Y Y N
N N Y Y Y N Y N Y N**
Answer: Regardless of which case holds, the result is that D scores 5 points.