Use assumptions, truth counts, implications, one-to-one matching, opposite-face reasoning, and complete case checks. Every puzzle and diagram needed for the exercise is included here; this lesson is not needed.
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Questions 1–10 · 6 points each · 60 points
A horse is either black, brown, or gray.
A: “I think it is not black.”
B: “It is either brown or gray.”
C: “I know it is brown.”
Among the three guesses, at least one is correct and at least one is wrong. What color is the horse?
The six faces of one cube are colored red, yellow, blue, white, black, and green. The three drawings show three views of the same face-color arrangement.
Five students A, B, C, D, and E are playing a Go tournament in which every pair of students plays one game. So far, A has played 4 games, B has played 3, C has played 2, and D has played 1. How many games has E played so far?
A, B, C, and D predict their Mathematics results:
A: “If I receive Excellent, then B also receives Excellent.”
B: “If I receive Excellent, then C also receives Excellent.”
C: “If I receive Excellent, then D also receives Excellent.”
All three statements are true, but exactly two students receive Excellent. Which two?
A pencil costs 0.5 yuan and an exercise book costs 0.4 yuan. Xiaoming spends 2.2 yuan altogether on pencils and exercise books. He buys a positive whole number of each item. How many of each does he buy?
For this puzzle, a piece of ore is classified as exactly one of iron, copper, or tin. A, B, and C each make two claims about it. Treat A’s “neither iron nor copper” as two claims: “not iron” and “not copper.”
A: “It is neither iron nor copper.”
B: “It is not iron; it is tin.”
C: “It is not tin; it is iron.”
Testing later shows that the experienced worker made both parts correctly, the trainee made both parts incorrectly, and the ordinary worker made exactly one part correctly and one incorrectly.
After Xiaoming, Xiaoqiang, and Xiaobing finish a race, they say:
Xiaoming: “I am first.”
Xiaoqiang: “I am second.”
Xiaobing: “I am not first.”
There are no ties: the three students finish first, second, and third. Exactly one student is lying. Determine the complete order.
A, B, C, D, and E take a test. Each score is a whole number from 0 through 10. All five statements below are true.
A: “I scored 4 points.”
B: “I scored higher than each of the other four students.”
C: “My score is the average of A's and D's scores.”
D: “My score is the average of all five scores.”
E: “My score is 2 points higher than C's, and I am the only student in second place.”
Xiaoming's phone number contains six different digits arranged from left to right in strictly decreasing order. Every two-digit number formed by two adjacent digits is divisible by 3. What is the phone number?
Three standard dice are stacked as shown. Only seven faces are visible. On each die, the numbers on opposite faces add to 7. Find the sum of the numbers on every face that cannot be seen from this viewpoint, including the faces touching another die and the bottom face resting on the surface.
Questions 11–13 · 20 points each · 60 points
A medical staff member says:
“Our hospital has 16 medical staff members in total, including me. Each is either a doctor or a nurse, and is counted as either male or female in this puzzle. Each statement below remains true both when I am included in the counts and when I am left out:
What are my sex and profession?”
Zhao, Qian, Sun, Li, and Zhou sit around a round table, all facing the center. “Left” means the seated person's own left. Because everyone faces the center, their immediate left neighbor is the next person clockwise when viewed from above. After dinner:
Zhou recalls: “Zhao sat next to Qian. The person immediately to Qian's left was either Sun or Li.”
Li recalls: “Qian sat immediately to Sun's left. I sat next to Sun.”
It turns out that all four individual claims are false. Determine the seating arrangement. The claim “either Sun or Li” is one claim: because it is false, neither Sun nor Li sits immediately to Qian’s left.
There are three bags:
The bags are labeled Red–Red, White–White, and Red–White, but every label is wrong. You may draw one ball from only one labeled bag. Explain how to determine the contents of all three bags.