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Mathematical Logic

Logic Warmups


Logic is the systematic study of argument. It is at the root of mathematics. Every piece of mathematics can be traced to basic logic.

Logic also happens to be a lot of fun, and many puzzles have logic at their core!

Melvin is taller than Nubia and Olly is taller than Melvin. Who is tallest and who is shortest?

Each row and each column in the puzzle below consists of the digits 1 to 3, each used in a particular row or column only once. Some digits have already been placed.

In addition, the inequality indicates that the digit in the upper left corner must be larger than the digit in the top middle square. When the puzzle is finished, which digit must go at the question mark?

Three children named Berita Blue, Remmy Red, and Greg Green have bikes that are blue, red and green in some order.

The child with the red bike says, "Did you notice none of us have a bike the same color as our last name?"

Greg Green responds, "Wow, that's strange!"

What color bike does Berita Blue ride?

In this game of Tic-Tac-Toe, you're playing X and your opponent is playing O. It's your turn. Assuming both players do the best moves possible, which move (a or b) will win the game?

In a certain village, each inhabitant is either a human or a werewolf. Humans always tell the truth and werewolves always lie.

Suppose (without being asked a question beforehand) someone makes this statement:

"I always lie."

Who could have said this?

Susan always tells the truth on weekdays (Monday to Friday) and always lies on weekends (Saturday and Sunday). Today, she says to you, “I will tell lies tomorrow.” What day(s) of the week could it be today?


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