Mathematics & Logic

Hard Logic Puzzle Challenge

Test your deductive reasoning with eight demanding logic problems that push mathematical thinking to the limit.

#logic puzzles#critical thinking#problem solving#brain workout#puzzle challenge#deductive logic#mathematical reasoning#hard brainteaser

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Total Questions

Difficulty Level

hard

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Quiz Questions

Answer all questions below and test your knowledge.

1
You have five face‑down cards, two red and three blue. You may flip exactly two cards. Which pair guarantees at least one red card?
Question 1
2
A 5‑digit number uses each digit 1‑5 exactly once. The sum of the first two digits equals the third digit. Which could be the number?
Question 2
3
In a circle, five points A‑E are placed clockwise. Chords AC and BD intersect inside the circle. Which statement must be true?
Question 3
4
Logic grid: Lara, Mike, Nina each own a different colored car (red, green, blue) and a different vehicle type (sedan, SUV, coupe). Lara does not own the red car. The SUV is blue. Mike drives the sedan. Which combination is possible?
Question 4
5
A 7‑segment display shows the digit 2. How many segments must be turned off to make the pattern unrecognizable as any decimal digit?
Question 5
6
Given statements: (P ∧ Q) → R is true, P is false, and R is false. What must be the truth value of Q?
Question 6
7
Sequence defined by a₁=1 and aₙ₊₁ = aₙ + (number of 1's in binary of aₙ). What is a₅?
Question 7
8
A farmer must transport a wolf, a goat, and a cabbage across a river. The boat holds the farmer plus one item. The wolf cannot be left alone with the goat, and the goat cannot be left alone with the cabbage. What is the minimum number of crossings required?
Question 8

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Hard Logic Puzzle Challenge

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Quiz Questions

You have five face‑down cards, two red and three blue. You may flip exactly two cards. Which pair guarantees at least one red card?

A 5‑digit number uses each digit 1‑5 exactly once. The sum of the first two digits equals the third digit. Which could be the number?

In a circle, five points A‑E are placed clockwise. Chords AC and BD intersect inside the circle. Which statement must be true?

Logic grid: Lara, Mike, Nina each own a different colored car (red, green, blue) and a different vehicle type (sedan, SUV, coupe). Lara does not own the red car. The SUV is blue. Mike drives the sedan. Which combination is possible?

A 7‑segment display shows the digit 2. How many segments must be turned off to make the pattern unrecognizable as any decimal digit?

Given statements: (P ∧ Q) → R is true, P is false, and R is false. What must be the truth value of Q?

Sequence defined by a₁=1 and aₙ₊₁ = aₙ + (number of 1's in binary of aₙ). What is a₅?

A farmer must transport a wolf, a goat, and a cabbage across a river. The boat holds the farmer plus one item. The wolf cannot be left alone with the goat, and the goat cannot be left alone with the cabbage. What is the minimum number of crossings required?

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