How can you add eight 8's to get the number 1,000? (only use addition)
Answer
The key to this math riddle is realizing that the one place must be zero.
888
+88
+8
+8
+8 =1,000
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
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.
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.
Answer to Riddle
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?
Answer to Riddle
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..
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 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 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?
Answer to Riddle
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. They they spent exactly $27 dollars.
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 ?
Answer
The answer is 4
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?
Answer
11 cartons total
7 large boxes (7 * 8 = 56 boxes)
4 small boxes (4 10 = 40 boxes
11 total cartons and 96 boxes
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)
Answer
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
Carrots
Fox
Rabbit
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
Carrots
Rabbit
(Not left alone)
Fox
Step 3) Take the carrots across.
Shore
Other Side
Rabbit
Fox
Carrots
Step 4) Go back and get the rabbit
Shore
Other Side
Rabbit
Fox
Carrots
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?
Answer
Every farmer's part is 1/3(45+75) = 40 sacks.
Charlie paid $1400 for 40 sacks, then 1 sack costs $1400/40 = $35/sack.
Adam got $35*(45-40)=35*5 = $175.
Ben got $35*(75-40)=35*35 = $1225.
Answer: Ben $1225, Adam $175
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.
Want a hint?
Why would he need to go back to get the last hint after seeing the number on the house next door?
Answer to hint
Because the sum of their ages ( the number on the house) is ambiguous and could refer to more than 1 trio of factors.
Answer to Riddle
Answer: { 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'.
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.
