# Math Puzzles

A collection of math puzzles for fun and pleasure! Tease your brain with these math puzzles,
then click to show or hide the answer.
(Note: You may need to enable JavaScript on your browser for the answers to show properly.)

Also visit our Math Trivia page for more arithmetic riddles, geometry riddles, statistics riddles, calculus riddles etc.

## The Two Watches

My husband and I can’t seem to get our watches working properly. His consistently runs one minute per hour fast, and mine runs two minutes per hour slow. This morning we nearly missed a wedding because our watches were an hour apart and we looked at the slower one. How many hours had elapsed since we set both of them properly?

20 hours.
## Cressida’s Age

Cressida didn’t like to tell her age, so when she was asked, her mother answered for her. Her mother said, “I’m just seven times as old as she is now. In twenty years, she will be just half the age that I will be then.” How old is clever little Cressida?

Cressida is four years old.
## Guess The Number

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second? (Hint: work backward.)

1349
## The Brave Knight

Our hero, the brave knight, is trying to rescue a beautiful princess. The fair maiden has slipped him a message. She will stand at the stable gate from 12.30 to 12.40 the following day, but no more than those ten minutes. If he arrives, she will elope with him. If not, she will be married that evening to the evil count. The castle is 12 miles away from the knight’s residence. The first third of the way is uphill, and the knight’s horse can run 4 mph uphill. The second third is level, at 8 mph, and the last third is downhill at 12 mph. The knight figures this averages to 8 miles an hour, so if he leaves at 10.55, he should arrive within those ten minutes. He can’t arrive too early, or he’ll be caught hanging around. Does he make it in time?

He doesn’t. He only arrives at 12.45. The poor Princess should have counted on someone who knows he shouldn’t just average speed and distance.
## Telephone Dial

This problem must not be solved by looking at the telephone. It is as much a test of your visual memory as a math puzzle. Add up all the numbers on the telephone dial, and then multiply that sum by all the numbers on the telephone dial. What do you get? (Average solving time is 30 seconds.)

0. Now you can look at the telephone and figure it out.
## Morning Run

You have decided to go for your morning run in preparation for the local marathon, and you are aiming for an average speed of 6 miles an hour. Unfortunately, you’re not in such good shape as you thought, and you find that you have completed the first half of your run – all uphill – at only 3 miles an hour. How fast must you run over the remaining downhill half to reach your target average speed?

It’s impossible. For example, if the run was 6 miles, you would have to finish in one hour to average 6 miles per hour. But you’ve already spent that hour covering the uphill half. You’ll just have to set more realistic goals.
## Acme Self-Igniting Gunpowder

Wile E. Coyote was at it again. He had just ordered an extra-large sack of Acme Self-Igniting Gunpowder, for the express purpose of blowing up that infernal Roadrunner. He did not realize, however, that the bag was leaking. He ran Roadrunner-style at 14 miles an hour trying to find the Roadrunner, but had to stop to rest after running 28 miles. Meanwhile, the self-igniting gunpowder was burning up his trail at 12 miles an hour. How long can he rest without his plan blowing up in his face?

He has 20 minutes.
## Short Yardstick

The owner of a fabric store had a yardstick, which was not, in fact, a yard long – it was 3 inches short. To make up for this and to prevent losing all his customers, he would add 5% to whatever yard goods he sold, which was usually enough. This time, however, Sally ordered 5 yards of curtain material. Was she short or over, and by how much? (Hint: The 5% extra is on his short yardstick, not a regular yard.)

Sally was short by 6.75 inches. She needed 180 inches, but the storeowner only gave her 165 inches plus 5% of that.

## Jogging or Strolling?

I don’t like health nuts. I refuse to do what is good for me. I stroll daily at 2 miles an hour. My jogger friend, however, has worked to change this, saying, “Why don’t you jog? You’d cover the same 12-mile distance, and you’d save a lot of time.” I notice that he jogs exactly 3 times as fast as I stroll. How much time will I save if I jogged with him?

I’d save 4 hours, not counting time spent unconscious from overexertion.
## The Louis XIV TV Set

As an antiques dealer, you are used to taking a loss every now and then. This is one of those times. The genuine Louis XIV TV set you bought has proved very difficult to sell. At first it was priced at $100, but you had to mark it down to $80. Then it was marked down to $64. How much will it cost after the next markdown? (You do realize that Louis XIV TV sets are difficult to sell – they aren’t state of the art, after all.)

It would cost $51.20. There was a 20% discount each time.

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