Logical Thinking Puzzles
Puzzle 1: The Counterfeit Coin
You have 12 coins, and one of them is counterfeit. The counterfeit coin is either heavier or lighter than the others. You have a balance scale and can only use it three times. How can you determine which coin is counterfeit and whether it’s heavier or lighter?
Answer: Divide the coins into three groups of four and use the balance to compare groups. Continue dividing and weighing until the counterfeit coin is isolated in three weighings.
Puzzle 2: The Fork in the Road
You’re traveling and come to a fork in the road. One path leads to treasure, while the other leads to doom. At the fork, there are two guards: one always tells the truth, and the other always lies. You’re allowed to ask only one question to one of the guards. What question would you ask to find the path to treasure?
Answer: Ask either guard, "If I asked the other guard which path leads to treasure, what would they say?" Then, take the opposite path.
Puzzle 3: Bridge Crossing in the Dark
Four people need to cross a bridge at night. They have one flashlight, and only two people can cross at a time. Each person walks at a different speed: 1 minute, 2 minutes, 5 minutes, and 10 minutes. When two people cross together, they must go at the slower person’s pace. How can all four cross the bridge in 17 minutes or less?
Answer: Crossing 1: A and B go (2 minutes), Return 1: A comes back (1 minute), Crossing 2: C and D go (10 minutes), Return 2: B comes back (2 minutes), Crossing 3: A and B go (2 minutes).
Puzzle 4: The Truth and Lies Island
You are on an island inhabited by two types of people: knights, who always tell the truth, and knaves, who always lie. You meet three islanders: A, B, and C. A says, "B and C are both knaves." B says, "A and C are both knights." C says, "A and B are different types." Who is who?
The solution that satisfies all statements is: A is a knight, B is a knave, C is a knave.
Puzzle 5: The Safe Combination
You need to crack a safe with a four-digit code. You know that:
- The first digit is a prime number.
- The second digit is a multiple of 2.
- The third digit is one greater than the second digit.
- The fourth digit is half the first digit.
Answer: 2011, 2231, 2451, 2671, 2891.
Puzzle 6: The River Crossing
A farmer has a wolf, a goat, and a cabbage. He needs to cross a river, but his boat can only carry him and one other item at a time. If left together, the wolf will eat the goat, and the goat will eat the cabbage. How can the farmer safely transport all three across the river?
Answer: Summary of Steps 1: Farmer takes goat across. 2: Farmer returns alone. 3: Farmer takes cabbage across. 4: Farmer brings goat back. 5: Farmer takes wolf across. 6: Farmer returns alone. 7: Farmer takes goat across.
