|

Solve 14 Challenging Mathematical Riddles with Solutions

By Isla Nguyen

Engaging with logical and mathematical riddles is an excellent way to sharpen your cognitive abilities and enhance problem-solving skills. These brain teasers vary in complexity, requiring creativity, reasoning, and sometimes a fresh perspective to uncover their solutions. Here’s a curated collection of mind-bending puzzles along with their answers.

Top Mathematical and Logic Riddles

This selection of riddles is designed to challenge your thinking and stimulate your mind.

1. Einstein’s Riddle

Often attributed to Albert Einstein, this logic puzzle’s true authorship is debated. It challenges deduction with the following scenario:

On a street, there are five houses of different colors, each occupied by a person of a different nationality. The five owners have distinct preferences: each drinks a specific beverage, smokes a particular brand of cigarette, and owns a unique pet. Given these clues:

  • The Brit lives in the red house.
  • The Swede has a dog.
  • The Dane drinks tea.
  • The Norwegian lives in the first house.
  • The German smokes Prince.
  • The green house is immediately to the left of the white house.
  • The owner of the green house drinks coffee.
  • The person who smokes Pall Mall keeps birds.
  • The owner of the yellow house smokes Dunhill.
  • The man in the center house drinks milk.
  • The neighbor who smokes Blends lives next to the one with a cat.
  • The man who owns a horse lives next to the one who smokes Dunhill.
  • The owner who smokes Bluemaster drinks beer.
  • The neighbor who smokes Blends lives next to the one who drinks water.
  • The Norwegian lives next to the blue house.

Who owns the fish?

2. Four Nines

A straightforward math puzzle: How can you use four nines to equal one hundred?

3. The Bear

This riddle tests geographical knowledge: A bear walks 10 km south, 10 km east, and 10 km north, returning precisely to its starting point. What color is the bear?

4. In the Dark

Imagine waking up in the middle of the night to find no lights working. You open your glove drawer, which contains ten black gloves and ten blue gloves. How many gloves must you pull out to guarantee you have at least one matching pair of the same color?

5. A Simple Operation

This riddle seems basic but requires a shift in perspective: When is the equation 11 + 3 = 2 correct?

6. The Twelve Coins Problem

You have twelve visually identical coins. Eleven weigh the same, but one is either slightly heavier or lighter. Using a balance scale, how can you identify the counterfeit coin and determine if it’s heavier or lighter in a maximum of three weighings?

7. The Knight’s Tour Problem

In chess, some pieces like the King and Queen can visit every square on the board. Others, like the Bishop, cannot. But what about the Knight? Can a knight move across a standard chessboard visiting every single square exactly once?

8. The Rabbit Paradox

An ancient and complex problem: Assume the Earth is a perfect sphere. If a rope is stretched perfectly around the equator, and then its length is increased by just one meter, creating a slightly larger circle, could a rabbit fit through the gap between the Earth and the rope?

9. The Square Window

This riddle asks: A nobleman had a hall with a single square window, 1m high by 1m wide. His poor eyesight meant the window let in too much light. He hired a builder to alter the window so it would only allow half the light in, but it had to remain square and still measure 1m by 1m. No curtains, colored glass, or other obstructions could be used. How could the builder solve this problem?

10. The Monkey Riddle

A monkey is hanging from one side of a simple, frictionless pulley. A weight, perfectly balancing the monkey, hangs from the other side. If the rope has no weight or friction, what happens if the monkey tries to climb up the rope?

11. Number Sequence

Solve the final equality in this pattern:

8806=6   7111=0   2172=0   6666=4   1111=0   7662=2
9312=1   0000=4   2222=0   3333=0   5555=0   8193=3
8096=5   7777=0   9999=4   7756=1   6855=3   9881=5
5531=0   2581=?

12. The Password

Police are observing a gang’s hideout. To enter, members use a password. One arrives, knocks, and hears “8” from inside. He replies “4,” and the door opens. Another arrives, hears “14,” replies “7,” and enters. An undercover agent attempts to infiltrate. He hears “6” and replies “3.” However, the door doesn’t open, and he receives fire. What is the trick to the password, and what mistake did the agent make?

13. What Number Follows the Series?

This riddle asks you to identify the number occupying a parking space in a series. The sequence is: 16, 06, 68, 88, ? (the occupied space you need to guess), and 98.

14. Operations

Complete the final operation in this sequence, which has two valid solutions:

1+4=5
2+5=12
3+6=21
8+11=?

Solutions to the Riddles

Curiosity satisfied? Here are the solutions to the puzzles above.

1. Einstein’s Riddle Solution

By systematically creating a table and using a process of elimination based on the clues, you can deduce the owner of each house, their nationality, drink, cigarette, and pet. The neighbor who owns the fish is the German.

2. Four Nines Solution

The solution is an elegant mathematical combination: 9/9 + 99 = 100.

3. The Bear Solution

The only place on Earth where walking 10 km south, then 10 km east, then 10 km north brings you back to your exact starting point is at the North Pole. Therefore, the bear must be a polar bear (white).

4. In the Dark Solution

To guarantee a matching pair, you must consider the worst-case scenario. You could pick one black glove and one blue glove (two gloves). The very next glove you pick, whether black or blue, will complete a pair. So, you need to pick 3 gloves.

5. A Simple Operation Solution

This operation is correct when referring to time. If it is 11 o’clock, and you add 3 hours, it will be 2 o’clock.

6. The Twelve Coins Problem Solution

This problem requires careful weighing:

  1. First weighing: Divide the coins into three groups of four (A, B, C). Place group A on one side of the balance and group B on the other.
    • If they balance, the fake coin is in group C.
    • If one side is heavier/lighter, the fake coin is in the heavier/lighter group, and you know if it’s heavier or lighter.
  2. Second weighing:
    • If the fake is in group C (balanced first weighing): Take three coins from C and three known good coins. Weigh them. If they balance, the remaining coin from C is fake. If they don’t balance, you know if it’s heavy or light.
    • If the fake was in A or B (unbalanced first weighing): Take three coins from the suspicious group and place two on the scale, one on each side, with one off the scale. Observe the balance to identify the fake and its weight difference.
  3. Third weighing: By this point, you will have narrowed it down to two or three coins, and based on the previous weighings, you’ll know if the fake is heavier or lighter. A final weighing will pinpoint the specific coin.

7. The Knight’s Tour Problem Solution

Yes, a knight can move across a standard 8×8 chessboard visiting every single square exactly once. This is known as a Knight’s Tour, and its possibility was proven by Leonhard Euler. There are many possible tours, one example of which is:

63 22 15 40 01 42 59 18
14 39 64 21 60 17 02 43
37 62 23 16 41 04 19 58
24 13 38 61 20 57 44 03
11 36 25 52 29 46 05 56
26 51 12 33 08 55 30 45
35 10 49 28 53 32 47 06
50 27 34 09 48 07 54 31

8. The Rabbit Paradox Solution

Yes, a rabbit could comfortably fit through the gap. Mathematically, if the Earth’s radius is ‘r’, the original rope length is 2πr. If the rope is extended by 1 meter, the new length is 2πr + 1. The new radius ‘R’ would be (2πr + 1) / (2π) = r + 1/(2π). The difference between the new radius and the old is 1/(2π), which is approximately 0.159 meters, or about 15.9 centimeters. This gap is wide enough for a rabbit to pass through.

9. The Square Window Solution

The builder can turn the square window into a diamond (rhombus) shape by orienting it diagonally. While its outer dimensions still measure 1m by 1m, the actual area allowing light to pass through would be halved, effectively reducing the light by half while maintaining its “square” nature (a rhombus is an oblique square).

10. The Monkey Riddle Solution

The monkey would reach the pulley. As the monkey climbs, its center of mass moves up. However, the system’s center of mass (monkey + rope + weight) remains constant because the monkey’s upward force on the rope is an internal force. The weight rises at the same rate as the monkey, effectively maintaining equilibrium until the monkey reaches the top.

11. Number Sequence Solution

The pattern counts the number of closed circles or “holes” in the digits of each number. For example, ‘8’ has two circles, ‘0’ has one, ‘6’ has one, ‘9’ has one.

  • 8806 has two ‘8’s (4 circles), one ‘0’ (1 circle), one ‘6’ (1 circle) = 4+1+1=6.
  • 7111 has no circles = 0.
  • 9999 has four ‘9’s (4 circles) = 4.
2

12. The Password Solution

The trick is not numerical division. The password is the number of letters in the spelled-out number.

  • EIGHT has 5 letters.
  • FOURTEEN has 8 letters.
  • SIX has 3 letters.

13. What Number Follows the Series? Solution

This puzzle simply requires you to view the parking lot from the opposite direction. If you were looking at the spaces from the other side, the numbers would be a standard numerical sequence in reverse. Looking at it upside down, the series is: 86, 87, 88, 89, 90, 91. Therefore, the occupied space is 87.

14. Operations Solution

There are two common valid solutions to this problem:

Solution 1: Accumulative Sum

Add the result of the previous line’s operation to the current line’s sum.

  • 1 + 4 = 5
  • 5 (previous result) + (2 + 5) = 12
  • 12 (previous result) + (3 + 6) = 21
  • 21 (previous result) + (8 + 11) = 40

Solution 2: Multiplication and Addition

Multiply the first number by the second number, then add the first number to that product.

  • 1 * 4 + 1 = 5
  • 2 * 5 + 2 = 12
  • 3 * 6 + 3 = 21
  • 8 * 11 + 8 = 96