Mathematics & Logic

Hard Logic Puzzles: Math Edition

A collection of ten challenging logic puzzles that require precise mathematical insight.

#logic#hard quiz#riddles#brain teaser#critical thinking#problem solving#math puzzles#deductive reasoning

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Total Questions

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hard

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Quiz Questions

Answer all questions below and test your knowledge.

1
A sealed box contains either a red, blue, or green marble. You draw one marble, see it is not red, and then replace it. The box still contains the same color marble. What is the probability that the marble is blue?
Question 1
2
In a row of six people, each either a knight who always tells the truth or a knave who always lies. Person 1 says, “Person 3 is a knave.” Person 3 says, “Person 5 is a knight.” Person 5 says, “Person 1 and Person 3 are of the same type.” Which person is a knight?
Question 2
3
A 3×3 magic square uses the numbers 1 to 9 each once. The center cell must be 5. Which of the following sets could be the numbers in the four corner cells?
Question 3
4
Five cards are placed face down. Exactly two are aces, one is a king, one is a queen, and one is a jack. You turn over three cards and see an ace, a king, and a queen. What is the probability that the remaining face‑down card is an ace?
Question 4
5
A river is 100 meters wide. A swimmer can swim 1.5 m/s in still water and the current flows at 0.5 m/s downstream. Starting from the opposite bank directly across from the starting point, she swims straight toward the starting bank (perpendicular to the current). How far downstream will she be carried when she reaches the opposite bank?
Question 5
6
In a group of 12 people, each person shakes hands with exactly three others. No pair shakes hands more than once. How many total handshakes occur?
Question 6
7
There are three boxes, each labeled incorrectly. One label reads “Apples”, another “Oranges”, the third “Apples and Oranges”. You may reach into one box, draw one piece of fruit, and see its type. Which box should you choose to correctly relabel all boxes?
Question 7
8
Consider the statement: ‘The next number in the sequence 2, 3, 5, 7, 11, ? is a prime that is also the sum of the two previous primes.’ Which number fits the description?
Question 8
9
A city has a bus schedule where bus A departs every 7 minutes, bus B every 9 minutes, and bus C every 11 minutes, all starting at 6:00 am. What is the earliest time after 6:00 am when all three buses depart together?
Question 9
10
Four statements: (1) Exactly one of these statements is true. (2) Statement 1 is false. (3) Statement 2 is true. (4) Statement 3 is false. Which statements are true?
Question 10

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Hard Logic Puzzles: Math Edition

Quiz Intelligence

Quiz Questions

A sealed box contains either a red, blue, or green marble. You draw one marble, see it is not red, and then replace it. The box still contains the same color marble. What is the probability that the marble is blue?

In a row of six people, each either a knight who always tells the truth or a knave who always lies. Person 1 says, “Person 3 is a knave.” Person 3 says, “Person 5 is a knight.” Person 5 says, “Person 1 and Person 3 are of the same type.” Which person is a knight?

A 3×3 magic square uses the numbers 1 to 9 each once. The center cell must be 5. Which of the following sets could be the numbers in the four corner cells?

Five cards are placed face down. Exactly two are aces, one is a king, one is a queen, and one is a jack. You turn over three cards and see an ace, a king, and a queen. What is the probability that the remaining face‑down card is an ace?

In a group of 12 people, each person shakes hands with exactly three others. No pair shakes hands more than once. How many total handshakes occur?

There are three boxes, each labeled incorrectly. One label reads “Apples”, another “Oranges”, the third “Apples and Oranges”. You may reach into one box, draw one piece of fruit, and see its type. Which box should you choose to correctly relabel all boxes?

Consider the statement: ‘The next number in the sequence 2, 3, 5, 7, 11, ? is a prime that is also the sum of the two previous primes.’ Which number fits the description?

A city has a bus schedule where bus A departs every 7 minutes, bus B every 9 minutes, and bus C every 11 minutes, all starting at 6:00 am. What is the earliest time after 6:00 am when all three buses depart together?

Four statements: (1) Exactly one of these statements is true. (2) Statement 1 is false. (3) Statement 2 is true. (4) Statement 3 is false. Which statements are true?

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Hard Logic Puzzles: Math Edition

Quiz Intelligence

Quiz Questions

A sealed box contains either a red, blue, or green marble. You draw one marble, see it is not red, and then replace it. The box still contains the same color marble. What is the probability that the marble is blue?

In a row of six people, each either a knight who always tells the truth or a knave who always lies. Person 1 says, “Person 3 is a knave.” Person 3 says, “Person 5 is a knight.” Person 5 says, “Person 1 and Person 3 are of the same type.” Which person is a knight?

A 3×3 magic square uses the numbers 1 to 9 each once. The center cell must be 5. Which of the following sets could be the numbers in the four corner cells?

Five cards are placed face down. Exactly two are aces, one is a king, one is a queen, and one is a jack. You turn over three cards and see an ace, a king, and a queen. What is the probability that the remaining face‑down card is an ace?

In a group of 12 people, each person shakes hands with exactly three others. No pair shakes hands more than once. How many total handshakes occur?

There are three boxes, each labeled incorrectly. One label reads “Apples”, another “Oranges”, the third “Apples and Oranges”. You may reach into one box, draw one piece of fruit, and see its type. Which box should you choose to correctly relabel all boxes?

Consider the statement: ‘The next number in the sequence 2, 3, 5, 7, 11, ? is a prime that is also the sum of the two previous primes.’ Which number fits the description?

A city has a bus schedule where bus A departs every 7 minutes, bus B every 9 minutes, and bus C every 11 minutes, all starting at 6:00 am. What is the earliest time after 6:00 am when all three buses depart together?

Four statements: (1) Exactly one of these statements is true. (2) Statement 1 is false. (3) Statement 2 is true. (4) Statement 3 is false. Which statements are true?

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A city has a bus schedule where bus A departs every 7 minutes, bus B every 9 minutes, and bus C every 11 minutes, all starting at 6:00 am. What is the earliest time after 6:00 am when all three buses depart together?