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# Mathematical Riddles

Mathematical riddles are a fun way to learn and practice the fundamentals of math without having to page through a dry textbook. There are math riddles for all ages and skill levels, and you don’t have to love math to have a good time solving them!

## Mathematical Riddles – Try Your Hand

Do you want to give your math skills a flex and try some math based riddles? See if you can figure out the following mathematical riddles. There is something here for all skill levels. The answers are below:

## Riddles:

- What number appears the most between 1 and 1,000?
- What number appears the least between 1 and 1,000?
- Two moms and two daughters shared three eggs, yet they each ate a whole egg. How could that have happened?
- Imagine that ½ of five is three. If that were true, what would 1/3 of ten equal?
- There is a hole that is six and half feet wide, five feet long and eight feet deep. How much dirt is in the hole?
- How can you make six nines equal 100? You can use any mathematical function to make the nines equal to 100, but you cannot use any other numbers.
- Imagine you have seven rings, divided into three interlocking sets. One set of rings contains four rings, one set contains two rings and there is one single ring left over to make up the third set. These rings can be used to be pay for a hotel room at the rate of one ring per night. You need to stay for seven nights, but the hotel won’t let you pay for any nights in advance, nor can you pay for your entire stay on the last night. How do you use your rings to pay for your room?
- You have a barrel of oil, a five-gallon container and a three-gallon container. You need to measure out four gallons. How do you do it?

## Answers:

- The number one appears most frequently between 1 and 1,000. In each set of tens between 1 and 1,000, each number zero – nine shows up once. (For instance, 30, 31, 32…). In the hundreds place, each number one – nine shows up an additional time – 301, 302, 303 and so on. If you include the initial one in the number 1,000, then one appears most frequently.
- The number that appears least frequently is zero. Every other number appears in a series (for instance, 22, 222 or 44, 444) and zero does not.
- One of the women is a grandmother, so she is both mother and daughter. There were only three women total eating eggs.
- According to that proportion, 1/3 of ten would be four.
- There is no dirt in the hole – otherwise it would not be a hole.
- 9 + 99/99 = 100
- Start by using the single ring to pay for your first night. On the second night, take that single ring back and give the hotel the set of two rings. On the third night, let the hotel keep the set of two rings and give them back the single ring. On the fourth night, take back the single ring and the set of two rings and turn over your set of four rings. On night five, let the hotel keep the set of four rings, and return the single ring to them. On the sixth night, let the hotel keep the four rings, give them the set of two rings and take back the single ring. On night seven, let them keep all the rings they have and return the single ring to them.
- Start by filling the three-gallon container with oil. Dump those three gallons into the five-gallon container. Refill your three gallon container, and pour as much as will fit into the five gallon container. That leaves you with one gallon left in your three-gallon container. Now, empty the five-gallon container and pour the one gallon from the three-gallon container into it. Refill the three-gallon container again and pour the contents into the five-gallon container. You now have four gallons in the five-gallon container.

## More Riddle Fun

If you enjoyed those mathematical riddles, there are much more you can try. These websites have good collections of math-based riddles:

**Heather McDonald**