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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)
The key to this math riddle is realizing that the one place must be zero.
888
+88
+8
+8
+8 =1,000
Math Riddle 2)
Two fathers and two sons sat down to eat eggs for breakfast. They ate exatly three eggs, each person had an egg. The riddle is fdor you to explain how
| How to Explain the Riddle |
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) (Two riddles in one)
Part I.What digit is the most frequent between the numbers 1 and 1,000?
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 occurance 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 hundres 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 occurance (301 occurences) compared to 2 or 3 or 9 which each have exactly 300 occurences.
The reason that zero has the least (BY FAR at only 192 occurences) is because zero does not have any equivelents to 22, 33, 44, 222, 3333 etc..
Riddle 4)
Three lawyers 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 lawysers 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 the 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 lawyers 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 ma ny ways of explaining/thinking bout 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 recieving $2 back).
If the lawyers get $3 back and each takes $1. They they spent exactly $27 dollars.
Math Riddle 5)
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
Math Riddle 6)
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 aremore 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
Other Great 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 mathematicains 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.
Crossing The River Riddle
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 becuase 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.
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Step 1) Take the rabbit to the other side
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| Shore |
Other Side |
Carrots
Fox
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Rabbit |
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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.
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| Shore |
Other Side |
Carrots
Rabbit
(Not left alone)
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Fox |
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Step 3) Take the carrots across. |
| Shore |
Other Side |
| Rabbit |
Fox
Carrots
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Step 4) Go back and get the rabbit |
| Shore |
Other Side |
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Rabbit
Fox
Carrots
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