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Math Riddles

Logic Games And Riddles

Riddle 1

How can you add eight 8's to get the number 1,000? (only use addition).

number 8 math riddle

The key to this math riddle is realizing that the one place must be zero. 888 + 88 + 8 + 8 + 8 = 1,000.

Riddle 2
Two Fathers and Two Sons Riddle

Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. The riddle is for you to explain how.

One of the 'fathers' is also a grandfather. Therefore the other father is both a son and a father to the grandson.

In other words, the one father is both a son and a father.

Riddle 3
Digit Frequency

Part I. What digit is the most frequent between the numbers 1 and 1,000 (inclusive)? To solve this riddle you don't want to manually do all of the math but rather try to figure out a pattern.

The most common digit is '1.' Can you figure out why? No hints until you try the next riddle because the next riddle is closely tied to this one.

Part II. What digit is the least frequent between the numbers 1 and 1,000?

0 is the least common digit even though 1,000 has three zero's!

Explanations for both riddles
The digits 0 through 9 all follow the same pattern there is exactly 1 occurrence of each digit for every ten numbers.

  • For instance the digit 2 appears once between 10 and 19, at 12. And 2 appears once between, 30 and 39 at 32.
  • However, each of the digits 1 through 9 also appear in other numbers in the tens and hundreds place.

Again, let's look at 2 which appears in 20, 21, 22, 23, etc.. as well as 200, 201, 202, 203.

So to figure out how to answer the first riddle you had to see what distinguishes the number 1? Only that we are including 1,000 which would be the first '1' in a new series of ten! In other words, the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which each have exactly 300 occurrences.

The reason that zero has the least (BY FAR at only 192 occurrences) is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc.

Riddle 4
Three Guys at A Hotel Riddle

Three guys rent a hotel room for the night. When they get to the hotel they pay the $$\$30 $$ fee, then go up to their room. Soon the bellhop brings up their bags and gives the lawyers back $$\$5$$ because the hotel was having a special discount that weekend. So the three lawyers decide to each keep one of the $$\$5$$ dollars and to give the bellhop a $$\$2$$ tip. However, when they sat down to tally up their expenses for the weekend they could not explain the following details:

Each one of them had originally paid $$\$10$$ (towards the initial $$\$30$$), then each got back $$\$1$$ which meant that they each paid $$\$9$$. Then they gave the bellhop a $$\$2$$ tip. HOWEVER, 3 • $$\$9$$ + $$\$2$$ = $$\$29$$.

The guys couldn't figure out what happened to the other dollar. After all, the three paid out $$\$30$$ but could only account for $$\$29$$.

Can you determine what happened?

There are many ways of explaining/thinking about this truly brain bending riddle! It all boils down to the fact that the lawyers's math is incorrect.

They did NOT spend $$\$9$$ • 3 + $$\$2$$.

They spent exactly $$\$27$$ dollars. $$\$25$$ for the room and $$\$2$$ for the tip. Remember they got exactly $$\$3$$, in total back.

Another way to think about the answer to this riddle is to just pretend that the bellhop refunded $$\$3$$ to the lawyers (rather than giving them $$\$5$$ and receiving $$\$2$$ back).

If the lawyers get $$\$3$$ back and each takes $$\$1$$. Then they spent exactly $$\$27$$ dollars.

Riddle 5
Foreign Country Riddle

In a certain country ½ of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10?

The answer is 4.

certain country riddle answers
Riddle 6
The Merchant

A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?

11 cartons total
7 large boxes (7 * 8 = 56 boxes)
4 small boxes (4 10 = 40 boxes
11 total cartons and 96 boxes

Riddle 7
Crossing the River

A farmer is trying to cross a river. He is taking with him a rabbit, carrots and a fox, and he has a small raft. He can only bring 1 item a time across the river because his raft can only fit either the rabbit, the carrots or the fox. How does he cross the river. (You can assume that the fox does not eat the rabbit if the man is present, you can also assume that the fox and the rabbit are not trying to escape and run away).

The key to solving this riddle is realizing that you have to take the rabbit over first and the switch the fox with the rabbit. See step 2.

Step 1

Take the rabbit to the other side.

Shore Other Side
Step 2

Go back and get the Fox and switch it with the Rabbit.
**The key here is that the carrots and the rabbit are not being left alone.

Shore Other Side
(Not left alone)
Step 3

Take the carrots across.

Shore Other Side
Rabbit Fox
Step 4

Go back and get the rabbit.

Shore Other Side
Riddle 8
Three Brothers on a Farm

Three brothers live in a farm. They agreed to buy new seeds: Adam and Ben would go and Charlie stayed to protect fields. Ben bought 75 sacks of wheat in the market whereas Adam bought 45 sacks. At home, they split the sacks equally. Charlie had paid 1400 dollars for the wheat. How much dollars did Ben and Adam get of the sum, considering equal split of the sacks?

Every farmer's part is $$1/3(45+75) = 40$$ sacks.
Charlie paid $$\$1400$$ for $$40$$ sacks, then 1 sack costs $$\$1400/40 = $35/{\text{sack}}$$.

Adam got $$\$35*(45-40)=35*5 = \$175$$.
Ben got $$\$35*(75-40)=35*35 = \$1225$$.
Answer: Ben $$\$1225$$, Adam $$\$175$$

Riddle 9
The Insurance Salesman

An insurance salesman walk up to house and knocks on the door. A woman answers, and he asks her how many children she has and how old they are. She says I will give you a hint. If you multiply the 3 children's ages, you get 36. He says this is not enough information. So she gives a him 2nd hint. If you add up the children's ages, the sum is the number on the house next door. He goes next door and looks at the house number and says this is still not enough information. So she says she'll give him one last hint which is that her oldest of the 3 plays piano.

Why would he need to go back to get the last hint after seeing the number on the house next door?

Because the sum of their ages (the number on the house) is ambiguous and could refer to more than 1 trio of factors.


{2, 2, 9}

If you list out the trio of factors that multiply to 36 and their sums, you get:

  • 1 1 36 = 38
  • 1 2 18 = 21
  • 1 3 12 = 16
  • 1 4 9 = 14
  • 6 6 1 = 13
  • 2 2 9 = 13
  • 2 3 6 = 11
  • 3 3 4 = 10

Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: { 6, 6, 1} , {2, 2, 9} . When she says her 'oldest' you know it can not be {6, 6, 1} since she would have two 'older' sons not an 'oldest'.

Riddle 10
The Monty Hall

This is a famous one. The classic Monty hall riddle!

The Situation: Picture of monty hall 3 doors Your First Choice

You are confronted by 3 doors. Behind one of them is a car, behind the two others, you will only see a goat. Now, if you correctly pick the car, you win the car! Otherwise, if you get one of the 2 goats, you don't get the car.

So, pick any door. It doesn't matter which one, but we will suppose that you picked door #2, as an example.

monty hall door Should You switch?

Now, after you have picked a door and before finding out what is actually behind it, you are shown a goat behind one of the other doors. (Remember there has to be a goat in 1 of the doors that you have not picked.)

Let's say you choose door #2, as shown above. For example's sake, let's say there's a goat in door 1. The question and the riddle is: should you switch the door that you picked? In other words, in this example, should you now choose door 3? Or, should you stick with your first choice (door #2)?

There actually is a mathematically correct answer to this riddle: You should indeed change your choice. If you don't believe me, just try out our free online Monty hall simulation.

Riddle 11

If 9999 = 4, 8888 = 8, 1816 = 6, 1212 = 0, then 1919 =


Look at how many closed areas there are.

  • 9999 has 4 closed areas (the top of the '9').
  • 8888 has 8 closed areas, the top and bottom parts of the 8 and there are no other digits.
  • 1816 has 3 closed areas, (top and bottom of 8 and bottom of 6, and it has 2 other digits (3 * 2 = 6)).
  • 1212 has 0 closed areas, (0 * 4 = 0).
Riddle 12

An athlete is able to jump FOREVER. However, everytime that she jumps she gets a bit more tired, and every jump goes $$ \frac 1 2 $$ as far as her prior jump. Now, for her very first jump, she goes $$ \frac 1 2 $$ of a foot.

On her second jump, she goes $$ \frac 1 4 $$ of a foot, and so on and so forth. The beginning of her journey is shown in the gif below.

zeno' paradox
How many jumps does it take for her to travel 1 foot?

She will never get to the 1 foot mark because you keep adding smaller and smaller amounts!

Other Good Riddles

Zeno's paradox of Achilles and the Tortoise

Quick summary of riddle: Zeno of Elea (490-425 BC) is known for creating many paradoxes which were debated by mathematicians for centuries. His riddle involving Achilles, the character from Homer's Iliad and a tortoise went something like:

The tortoise challenged Achilles to a race and Achilles, full of typical hubris, accepted and even gave the Tortoise a 10 foot head start. Before the race started, the tortoise told Achilles that the reason Achilles would lose is that even though Achilles would be catching up, the tortoise would always be moving ahead. Therefore, Achilles would always be covering a fraction of the distance between the two. Let's say he covered half of the distance in 1 second (5 feet) and then in the next he covered half of the new distance, the remaining 5 feet plus the Tortoise's new distance. In the end, the tortoise convinced Achilles that he could not win the race because although he would be getting closer and closer, he would still always be covering smaller and smaller fractions of the total distance between the two. Therefore, Achilles forfeited the race. To read this riddle in a modern narrative form click here.

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