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Logical Reasoning

How can you find a fake coin with a balance scale? How can you use math to pretend to read minds? Solve these puzzles and build your foundational logical reasoning skills.

Level 2

         

The figure shows 3 glasses filled with water and 3 empty glasses (top of figure).

With just your hands, what is the minimum number of glasses you have to pick up in order to make the bottom arrangement?

Note: No sliding of glasses is allowed. You can pour the water from one glass to another.

You are given 80 eggs and given the following information

All the eggs except one are of identical weights. The exceptional egg is lighter.

Using a weighing balance, you must find that particular egg. What is the minimum number of weighings that is needed to guarantee to identify the egg?


Inspiration.

The problem and its solution for general case was found in collaboration with Abhijit Bendre.

James and Jonathan lie on specific days.

James lies on Fridays, Saturdays and Sundays, but he is honest on all other days.

Jonathan lies on Tuesdays, Wednesdays and Thursdays, but he tells the truth on all other days.

On what day of the week would they both say "Tomorrow, I will lie."?

You are presented with 3 chests:

Chest A has been labelled with "100 gold coins."
Chest B has been labelled with "50 gold and 50 silver coins."
Chest C has been labelled with "100 silver coins."

You are told that each label is incorrectly placed because it describes the contents of another chest. To help you determine which chest truly contains 100 gold coins, you are allowed to randomly pick a coin from any chest.

Which chest should you pick a coin from?

There are 3 boxes, exactly one of which has a car. You can keep the car if you pick the correct box!

On each box there is a statement, exactly one of which is true.

Box 1: The car is in this box.
Box 2: The car is not in this box.
Box 3: The car is not in box 1.

Which box has the car?

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