# Logic Puzzles

## Featured Puzzle

There are three boxes: one contains all apples, one contains all oranges, and one contains both. They are labeled “apples”, “oranges”, and “apples and oranges” but all 3 boxes were labeled incorrectly!

The boxes look the same on the outside, but you can take out fruit one at a time from any box. What is the fewest number of fruit you need to inspect to fix all the labels?

• ## Fake Coins Proof

You are a rare coins expert and have determined there are 7 fake coins out of 14 gold coins. Now you need to prove to the judge which ones are fake.

It is known that that real coins all weigh the same, fake coins all weigh the same, and fake coins weigh less than real ones (but are otherwise identical).

Using a traditional double-pan balance scale just 3 times, can you prove exactly which of the 14 coins are fake?

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• ## Escape the Maze

In this maze of 8×8 rooms, each room has an arrow that points up, down, left, or right – and it will only let you move to the adjacent room in the direction of the arrow.

After you leave a room, or if you are unable to move because there is no adjacent room in the direction of the arrow (i.e., the arrow points outside the maze but there is no exit), the arrow in that room will rotate 90 degrees clockwise.

You start in the bottom left room, and the only exit is the right door in the top-right room.

Prove that no matter what the initial arrangement is, you will eventually escape the maze.

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• ## Four-Card Problem

You see four cards with A, D, 3, and 6 face-up. You know that each card has a letter on one side and a number on the other side.

You are told that cards with a vowel on one side must have an even number on the other side. Which cards do you need to turn over to test if this rule is broken?

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• ## 3 Digit Code

You have six guesses to figure out a 3 digit code. After each guess, you will be told exactly how many digits are correct but in the wrong place and how many digits are correct and in the right place. You have made these five guesses already:

• 865: exactly one digit in the right place
• 964: exactly one correct digit but in the wrong place
• 983: no correct digits
• 548: exactly two correct digits but in the wrong places
• 812: exactly one correct digit but in the wrong place

What is the correct 3 digit code?

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• ## Guess the Number

Jake has a 4-digit number in mind and asks Raj to guess the number. Raj can have 7 guesses, and Jake will give him some hints after 6 guesses.

Raj makes these 6 guesses:

• 6 3 5 8
• 9 3 0 6
• 4 8 8 2
• 6 7 2 8
• 1 1 9 1
• 5 6 2 7

These were all wrong, but Jake says every guess had exactly one (and only one) correct digit in the correct position. Additionally, all the digits are different.

What should Raj’s 7th guess be?

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• ## Last Chocolate Game

Two friends are playing a game with two boxes of chocolates. They take turns taking out some number of chocolates from the boxes, and whoever takes the last chocolate wins. Each turn they can take chocolates one of two ways:

• Take any number of chocolates from a single box
• Or take an equal number of chocolates from each box

If there are 25 chocolates in one box and 35 in the other, what is the winning strategy?

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• ## Who is Lying?

Chris says both Amy and Brad are lying.

Who is lying? Who is telling the truth?

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• ## Random Turns

You are in a city with streets on a perfect grid – every street is north-south or east-west. You are are driving north, and decide to randomly turn left or right with equal probability at the next 10 intersections.

After these 10 random turns, what is the probability you are still driving north?

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• ## Water Jug Riddle

You have a 3-litre jug and a 5-litre jug, and as much water as you need. How do you measure out exactly 4 litres using only these two jugs?

This is a classic logic puzzle, sometimes used in finance and engineering interviews many years ago. It also was featured in the movie Die Hard with a Vengeance!

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• ## Impossible Sudoku

You may be familiar with Sudoku, a combinatorial number placement puzzle in which you fill in a 9×9 grid with digits such that each row, column, and 3×3 square contains all of the digits 1-9 exactly once.

You come across a Sudoku puzzle in which the initially populated numbers appear to be legal (no row, column, or square had the same number twice), but it is clear that trying to solve the puzzle would lead to an impossible arrangement of numbers – an unsolvable puzzle not because there is not enough information, but because it forces you into a contradictory/rule-breaking result. What is the smallest possible sum of the initial numbers?

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