Mary's ideal “Prince Charming” is tall, has dark skin, and is handsome. Among Mike, Bill, John, and Jack, exactly one man satisfies all three conditions.

1. Exactly three of the four men are tall, exactly two have dark skin, and exactly one is handsome.
2. Every man satisfies at least one of the three conditions.
3. Mike and Bill have the same skin-color status: either both have dark skin or neither does.
4. Bill and John have the same height status: either both are tall or neither is.
5. John and Mike are not both tall.

Who satisfies all three conditions?

A 24-hour electronic clock shows hours from 00 through 23 and minutes from 00 through 59. Ignore the colon and read the four digits HHMM. Count a time when its display contains a run of at least three identical consecutive digits.

Examples include 00:0000:0503:3311:1220:0022:22.

How many minute displays in one full day have this property? Count each minute once, even when runs of repeated digits overlap.

Is Xiaohong correct?

The sum of two numbers is 75. The first number is 15 greater than the second number. What is the second number?

Floors are numbered 1 at the bottom through 4 at the top. A, B, C, and D live on different floors of a four-story building and have four different occupations: engineer, worker, teacher, and doctor.

1. A lives above B but below C. D lives on the fourth floor.
2. The doctor lives above the teacher but below the worker. The engineer lives on the first floor.

Complete every person's floor and occupation.

A, B, C, D, and E play a table-tennis round robin: every pair plays exactly one match, with no draws. A winner receives 2 points and a loser receives 0.

• A and E tie for first place.
• B is third.
• C and D tie for fourth place.

How many points does B have?

There are three bags. One contains candy; each of the other two contains one stone. The labels say:

The statement on the candy bag is true. Among the other two statements, at least one is false. Which bag contains the candy?

Four cards carry the four different Chinese characters 努, 力, 学, and 习. Three of the four cards are selected and placed face down as Card 1, Card 2, and Card 3. No knowledge of Chinese is needed; treat the characters as four distinct symbols.

Every card is guessed correctly by at least one person. Of the three guessers, one gets none of the three cards correct, while the other two get exactly two and exactly three correct, respectively. What is on each card?

Choose five distinct numbers A, B, C, D, E from the integers 1 through 10 so that all six conditions hold:

1. D is greater than 6.
2. D is divisible by C.
3. A + D = B.
4. A + C + E = D.
5. A + C < E.
6. A + E < C + 5.

List every ordered solution (A, B, C, D, E) that satisfies all conditions.

A, B, C, D, and E are the top five students, with no ties, and predict their ranks:

Each predictor guesses exactly one person's rank correctly, and each rank is correctly identified by exactly one predictor. Determine the actual ranking.

Mr. and Mrs. A invite three other married couples—B, C, and D—to dinner. The eight people sit around a circular table. Exactly one married couple is not seated together. “Together” means in immediately neighboring seats, including the neighbors across the end of the numbered list.

1. The person opposite Mrs. A is the gentleman seated immediately to the left of Mr. B.
2. The person immediately to the left of Mrs. C is a woman seated opposite Mr. D.
3. The person immediately to the right of Mr. D is a woman. She sits opposite the woman who is two seats to the left of Mr. A.

Everyone faces the center. “Left” and “right” refer to the seated person's own left and right: with everyone facing inward, left is clockwise and right is counterclockwise. Clockwise order is viewed from above; the numbered seats below run clockwise. Which married couple is separated?

Aunt Zhang asks three young workers—Xiao Liu, Xiao Chen, and Xiao Li—their ages. Each person makes three statements, and exactly one of each person's three statements is false.

Determine their ages in whole years. Treat “differ by 3” as larger age minus smaller age equals 3.

Teams A, B, C, and D play a football round robin, so every pair of teams plays one match. A win is worth 2 points, a draw 1 point, and a loss 0 points.

• B earns 5 points, C earns 3 points, and A earns 1 point.
• There are 9 goals in all six matches combined.
• B scores more goals than any other team, with 4 goals in total.
• C concedes 3 goals in total.
• D scores no goals.
• The score in the A–C match is A:C = 2:3.

What is the score in the A–B match?