# 30 Math Riddles

Mathematics is not just about solving equations and doing calculations; it can also be a lot of fun! Math riddles are a fantastic way to engage your brain and enjoy the beauty of these numbers.

In this blog post, we’ll explore some math riddles that will make you think, laugh, and maybe even scratch your head.

Letâ€™s begin.

## Math Riddles

**The Missing Dollar**: Three friends check into a hotel room that costs $30. Each friend pays $10. Later, the hotel clerk realizes there’s a special rate for the room at $25. The clerk gives $5 to the bellboy to return to the friends. The bellboy, however, gives each friend $1 and keeps $2 for himself. Now, each friend paid $9, totaling $27, and the bellboy has $2. That makes $29. Where is the missing dollar?**The Age Puzzle**: I am twice as old as my friend was when I was as old as my friend is now. Together, our ages total 63 years. How old am I and how old is my friend?**The Lilies in the Pond**: A pond has a single lily pad. Each day, the number of lily pads doubles. If the pond is completely covered with lily pads on the 48th day, on what day was the pond half covered?**The Mysterious Numbers**: Think of a number. Multiply it by 3. Add 6 to the result. Divide this number by 3. Subtract the original number. What’s the result?**The Infamous Monty Hall**: In a game show, you’re given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, revealing a goat. He then asks you if you want to switch to door No. 2. Should you switch?**The Birthday Paradox**: In a room of 23 people, what’s the probability that two people have the same birthday?**The Unusual Sum**: What is the sum of the numbers from 1 to 100?**The Chessboard Rice Problem**: A king agrees to pay a wise man by placing 1 grain of rice on the first square of a chessboard, 2 grains on the second, 4 on the third, and so on, doubling the number of grains on each subsequent square. How many grains of rice are there on the chessboard when it’s fully covered?**The Three Gods Riddle**: There are three gods A, B, and C. One always tells the truth, one always lies, and one answers randomly. You can ask three yes-or-no questions to determine which god is which. What questions do you ask?**The Frog in the Well**: A frog falls into a well that’s 30 feet deep. Each day, the frog climbs 3 feet but slides back 2 feet at night. How many days does it take the frog to get out of the well?**Dividing the Cake**: You have a cake and exactly 3 cuts to divide it into 8 equal pieces. How do you do it?**The Farmer’s Dilemma**: A farmer has 17 sheep, all but 9 die. How many are left?**The Mysterious Coin**: I have a coin that when heads is facing up, the chance of flipping tails is 50%. What are the odds it will land on tails if it is currently on heads?**The Clock Puzzle**: How many times a day do the hour and minute hands of a clock overlap?**The Number Sequence**: What comes next in the sequence: 1, 11, 21, 1211, 111221, …?**The Bridge Crossing**: Four people need to cross a rickety bridge at night. They have one flashlight and can only cross two at a time. The bridge can only hold their weight for 17 minutes. Their walking speeds are 1 min, 2 mins, 5 mins, and 10 mins. How can they all cross in 17 minutes?**The 100 Floors Puzzle**: You have two eggs and access to a 100-story building. The eggs can survive falls from certain floors but not others. What’s the least number of drops you need to find out the highest floor from which an egg can fall without breaking?**The Tricky Multiplication**: If 1/2 of 5 is 3, then what is 1/3 of 10?**The Infinite Hotel**: A hotel has an infinite number of rooms and all of them are occupied. How can it accommodate an additional infinite number of guests?**The Weighing Scale Puzzle**: You have 9 balls of equal size. 8 balls weigh the same, and one is slightly heavier. How can you find the heavier one using a balance scale only twice?**The Missing Fish**: Five fishermen caught 5 fish in 5 minutes. At this rate, how many fish can they catch in 60 minutes?**The Square Meal**: If you have a square pizza, and you cut it with two straight lines through its center, how many pieces can you make?**The Classic 3 & 5 Liter Puzzle**: You have a 3-liter jug and a 5-liter jug, how can you measure out exactly 4 liters?**The Digital Clock Conundrum**: A digital clock displays hours and minutes. How many times in a day does it display three or more of the same number in a row?**The Numbers in the Locker**: A high school has 1,000 lockers and 1,000 students. The first student opens all the lockers. The second student closes every second locker. The third student changes the state (open/close) of every third locker, and so on, up to the 1,000th student. Which lockers are open at the end?**The Snail in the Well**: A snail climbs a 10-foot wall. Each day it climbs 3 feet but slides back 2 feet each night. How many days does it take to reach the top?**The Four 4s**: Using exactly four 4s and any math operations, can you make the number 55?**The Reverse Age Riddle**: Ten years ago, my age was the reverse of what it is now. How old am I?**The Coin Toss Puzzle**: If you flip a fair coin three times, what is the probability of getting at least one head?**The Socks in the Dark**: In a drawer, there are 10 black socks and 10 white socks. If you’re in a dark room and can only take one sock at a time, how many socks must you take to ensure you have a matching pair?

## Answers

**The Missing Dollar**: The friends paid $27 ($25 for the room and $2 for the bellboy). There’s no missing dollar.**The Age Puzzle**: I am 42 years old, and my friend is 21 years old.**The Lilies in the Pond**: On the 47th day, as the lily pads double each day.**The Mysterious Numbers**: The result is always 2.**The Infamous Monty Hall**: Yes, you should switch. The chance of winning the car increases to 2/3 if you switch.**The Birthday Paradox**: About 50.7%.**The Unusual Sum**: 5050 (This can be calculated using the formula for the sum of an arithmetic series).**The Chessboard Rice Problem**: There are 2^64 – 1 grains of rice, which is 18,446,744,073,709,551,615 grains.**The Three Gods Riddle**: This is a complex logic puzzle, and the questions depend on the responses and could vary. A common strategy involves using conditional statements to determine the truth-teller or the liar.**The Frog in the Well**: On the 28th day, the frog reaches 27 feet and climbs 3 feet on the 29th day to get out, without sliding back.**Dividing the Cake**: First cut the cake into two equal parts. Stack one half over the other and make the second cut horizontally. Now, cut through the stacked pieces perpendicular to the first cut.**The Farmer’s Dilemma**: 9 sheep are left.**The Mysterious Coin**: The odds remain 50%.**The Clock Puzzle**: The hands overlap 22 times a day.**The Number Sequence**: The next number is 312211 (the sequence describes the count of the numbers before it).**The Bridge Crossing**:- First, the 1 and 2-minute people cross, taking 2 minutes.
- The 1-minute person comes back with the flashlight, taking 1 more minute (total 3 minutes).
- The 10 and 5-minute people cross, taking 10 minutes (total 13 minutes).
- The 2-minute person returns with the flashlight, taking 2 more minutes (total 15 minutes).
- Finally, the 1 and 2-minute people cross again, taking 2 minutes (total 17 minutes).

**The 100 Floors Puzzle**: Start from the 14th floor and go up 14 floors at a time. This way, the maximum number of drops is 14.**The Tricky Multiplication**: 5. The phrase “1/2 of 5 is 3” is a riddle in itself. The ‘3’ comes from the fact that when you split the number ‘5’ in half, you get the numbers ‘2’ and ‘3’.**The Infinite Hotel**: Move the guest in room 1 to room 2, room 2 to room 4, and so on. Every guest moves to a room number twice their current room number. This frees up all odd-numbered rooms for the new guests.**The Weighing Scale Puzzle**:

- First, divide the balls into 3 groups of 3.
- Weigh two groups against each other. If they balance, the heavier ball is in the third group. If not, it’s in the heavier group.
- Weigh two balls from the heavier or suspected group. If they balance, the third ball is the heavier one. If not, the heavier side shows the heavier ball.

**The Missing Fish**: They can catch 60 fish. The rate is 5 fish every 5 minutes, so in 60 minutes, it would be 60 fish.**The Square Meal**: You can make 4 pieces with 2 cuts.**The Classic 3 & 5 Liter Puzzle**: Fill the 5-liter jug, pour 3 liters into the 3-liter jug, leaving 2 liters in the 5-liter jug. Empty the 3-liter jug and pour the 2 liters into it. Fill the 5-liter jug again and pour enough to fill the 3-liter jug, which will leave 4 liters in the 5-liter jug.**The Digital Clock Conundrum**: The digital clock displays three or more of the same number in a row 34 times a day.**The Numbers in the Locker**: Lockers that are open are those which are perfect squares (1, 4, 9, 16, …, 961, 1024).**The Snail in the Well**: It takes 8 days. On the 8th day, the snail climbs 3 feet and reaches the top without sliding back.**The Four 4s**: 44 + 4 + 4/4 = 55.**The Reverse Age Riddle**: I am 21 years old. (11 years ago, I was 10).**The Coin Toss Puzzle**: The probability is 7/8. The only way to not get a head is to get three tails, which has a 1/8 chance, so getting at least one head is 1 – 1/8 = 7/8.**The Socks in the Dark**: You must take out 3 socks. The first two could be one of each color, but the third will definitely match one of them.