# Logic Puzzles

Classic logic puzzles in which you infer or deduce actions and outcomes based on information provided

## Number of True Statements

Which of the following statements are true?

1. The number of true statements is 0 or 1 or 3.
2. The number of true statements is 1 or 2 or 3.
3. The number of true statements (excluding this one) is 0 or 1 or 3.
4. The number of true statements (excluding this one) is 1 or 2 or 3.
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## Honkai Star Rail Dissatisfied Cycrane Truth and Lie Riddle

In Honkai: Star Rail, one side quest takes you to solve a number of puzzles involving cycranes, including one fun and tricky Dissatisfied Cycrane truth and lie riddle!

“I either can only tell the truth, can only tell lies, or must say a lie after a truth. You can only ask two questions, and then I’ll ask for your answer.”

—Dissatisfied Cycrane

## 6 Tricky Lying Thief Riddles

These lying thief riddles are fun and tricky logic puzzles that will test your brain. In each puzzle, you interrogate a number of suspects, knowing that some of them are lying, and use that information and your deduction skills to find the true culprit.

## Lying Thief Riddle #1 (Easy)

There are 3 suspects in a robbery, one of which is the true culprit:

• A: “I didn’t do it.”
• B: “C did it.”
• C: “B is lying.”

You know that two suspects are lying and one is telling the truth. Who is guilty?

## Favorite Fruit and Favorite Color

Ava, Beth, Cam, and Derek each have a different favorite fruit and favorite color. We know their favorite fruits are apple, banana, cherry, and durian, and their favorite colors are blue, green, red, and yellow. We also know:

1. Cam does not like apples or cherries
2. Derek’s favorite color is yellow and his favorite fruit is not banana
3. The person whose favorite fruit is cherry also likes the color green
4. Beth’s favorite color is red and her favorite fruit is not apple
5. The person whose favorite fruit is durian does not like the color blue

What is each person’s favorite fruit and favorite color?

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## Color of the Last Ball

There is a bag with 20 blue balls and 13 red balls. Randomly remove 2 balls from the bag:

• If they are the same color, replace them with a blue ball
• If they are different colors, replace them with a red ball

Repeat this process until there is just 1 ball remaining. What is the color of the last ball?

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## Prison Keys Strategy

A prison warden was feeling capricious and played a game with the prison keys:

1. Each prisoner is handed a key to another prisoner’s cell.
2. Each prisoner will know which other prisoner was initially given the key to their cell (but does not know whose key they were handed).
3. Each day, when all prisoners are out of their cells and no one is watching, each prisoner is allowed to place keys in another prisoner’s cell.
4. Each night, each prisoner can collect any keys placed in their cell.
5. The prisoners can summon the warden when they’re sure everyone has their own key – but if they are wrong, they’re immediately executed.
6. The prisoners can discuss a strategy beforehand but cannot communicate in any way after keys are handed out.

What is the fewest number of days it would take for the prisoners to be sure everyone has their key? What was the strategy to achieve this?

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## Sharing Game Theory Puzzle

In this sharing game theory puzzle, 3 friends take turns taking from a jar of 1000 candies to share. For example, the 1st friend could take 500 candies, then the 2nd friend could take 400, and the 3rd friend would take the remaining 100.

No one wants to be seen as greedy, but no one wants to end up with the fewest candies either. As such, their goals are (in order of preference):

1. Do not end up with the most candies, nor the fewest candies (a tie for most or fewest also fails this condition)
2. End up with as many candies as possible

All of them are logical, rational, know each other’s goals, but cannot communicate before or during sharing. How many candies should each friend end up with?

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## The Impossible Puzzle

This puzzle was coined the “Impossible Puzzle” by Martin Gardner, a famous math and science writer that liked to create and write about math games and puzzles. The puzzle is named as such because it appears to provide insufficient information to solve, but it is in fact solvable! Read on for the puzzle and the (very difficult) solution.

There are two distinct whole numbers greater than 1, we can call them x and y (where y > x). We know the sum of x and y is no more than 100.

Sam and Prada are perfect logicians. Sam (“sum”) is told x + y and Prada (“product”) is told x * y, and both of them know all the information provided so far.

Sam and Prada have this conversation in which they truthfully deduce the numbers:

1. Sam: I know Prada does not know x and y.
2. Prada: Well now I know x and y.
3. Sam: Ah, now I also know x and y.

Can you figure out x and y using this information?

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## Lions and Sheep

On a magical island, there are 100 lions and 1 sheep, all of which can live by eating the plentiful grass on the island. Any lion that eats the sheep will magically turn into a sheep afterward, such that there will always be a sheep on the island.

Every lion would like to eat a sheep, but would much rather prefer to not be eaten (they wouldn’t mind turning into a sheep if they wouldn’t be eaten).

If all the lions act rationally and know all the other lions act rationally, how many lions will remain on the island in the end?

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## Number Deduction

A teacher gives three clever students in her class a challenge: she writes down 3 different numbers on 3 index cards, and has each student hold up one of the cards to their forehead such that they can’t see their own card but everyone else can.

She tells them each card has a different number, and that two of the numbers add up to the third number, and asks them to figure out their number without sharing the numbers they see.