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# Math Playground

## Math Playground

Welcome to Math Playground where you can test your math skills by solving a few fun brain teasers.
No worries, you just need to know the basics and think logically. Even kids can solve these puzzles.

One brick is one kilogram and half a brick heavy.
What is the weight of one brick?

## Fly

Two trains, 200 km apart, are moving toward each other at the speed of 50 km/hour each. A fly takes off from one train flying straight toward the other at the speed of 75 km/hour. Having reached the other train, the fly bounces off it and flies back to the first train. The fly repeats the trip until the trains collide and the bug is squashed.
What distance has the fly traveled until its death?
There is a complicated and an easy way to calculate this cool math puzzle.
Think outside the box.

## Trains

A passenger train leaves New York for Boston traveling at the speed of 80 km/hr. In half an hour a freight train leaves Boston for New York traveling at the speed of 60 km/hr.
Which train will be further from New York when they meet?

## Speeding up

Let's play a game. If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?

## Wired Equator

The circumference of the Earth is approximately 40,000 km. If we made a circle of wire around the globe, that is only 10 meters (0.01 km) longer than the circumference of the globe, could a flea, a mouse, or even a man creep under it?

## Cool Math Play by Diophantus

We know little about this Greek mathematician from Alexandria, called the father of algebra, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life.
Diophantus's youth lasted 1/6 of his life. He had his first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.
How long did Diophantus live?

## Ahmes's Papyrus

About 1650 B. C., Egyptian scribe Ahmes, made a transcript of even more ancient mathematical scriptures dating to the reign of the Pharaoh Amenemhat III. In 1858 Scottish antiquarian, Henry Rhind came into possession of Ahmes's papyrus. The papyrus is a scroll 33 cm wide and about 5.25 m long filled with funny math riddles. One of the problems is as follows:
100 measures of corn must be divided among 5 workers, so that the second worker gets as many measures more than the first worker, as the third gets more than the second, as the fourth gets more than the third, and as the fifth gets more than the fourth. The first two workers shall get seven times less measures of corn than the three others.
How many measures of corn shall each worker get? (You can have fractional measures of corn.)

## Midnight

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later.
What time is it now?

## Clock

At noon the hour, minute, and second hands coincide. In about one hour and five minutes the minute and hour hands will coincide again.
What is the exact time (to the millisecond) when this occurs, and what angle will they form with the second hand?
(Assume that the clock hands move continuously.)

## Filling the Pool

A swimming pool has four faucets. The first can fill the entire pool with water in two days, the second - in three days, the third - in four days, and the last one can fill the pool in 6 hours.
How long will it take to fill the pool using all 4 faucets together?

## The Castle

A square medieval castle on a square island is under siege. All around the castle there is a square moat 10 meters wide. Due to a regrettable miscalculation the raiders have brought footbridges, which are only 9.5 meters long. The invaders cannot abandon their campaign and return empty-handed.
How can the assailants resolve their predicament?

Just a little side note. "The Castle" puzzle reminds me of another cool math joke - student's answer on a math test where "x" should have been found.

## Crossing the Desert

A military car carrying an important letter must cross a desert. There is no petrol station in the desert, and the car's fuel tank is just enough to take it half way across. There are other cars with the same fuel capacity that can transfer their petrol to one another. There are no canisters or rope to tow the cars.
How can the letter be delivered?
You can play a little game with model cars to simulate this puzzle.

## Airplanes

A distant planet "X" has only one airport located at the planet's North Pole. There are only 3 airplanes and lots of fuel at the airport. Each airplane has just enough fuel capacity to get to the South Pole. The airplanes can transfer their fuel to one another.
Your mission is to fly around the globe above the South Pole with at least one airplane, and in the end, all the airplanes must return to the airport.

## Magic Belt

A magic wish-granting rectangular belt always shrinks to 1/2 its length and 1/3 its width whenever its owner makes a wish. After three wishes, the surface area of the belt's front side was 4 cm2.
What was the original length, if the original width was 9 cm?

## Cost of War

Here's a variation on a famous puzzle by Lewis Carroll, who wrote Alice's Adventures in Wonderland.
A group of 100 soldiers suffered the following injuries in a battle: 70 soldiers lost an eye, 75 lost an ear, 85 lost a leg, and 80 lost an arm.
What is the minimum number of soldiers who must have lost all 4?

## Bavarian

One glass has 10 cl of tonic water and another 10 cl of fernet. Pour 3 cl of tonic into the glass with fernet and after mixing thoroughly, pour 3 cl of the mixture back into the glass with tonic water.
Is there more tonic in the glass of fernet or more fernet in the glass of tonic?
(Ignore the chemical composition!)

## What is Correct

Is it correct that seven and five is thirteen or seven and five are thirteen?

## Strange Coins

I have two US coins totaling 55 cents. One is not a nickel.
Figure out what the coins are.

## Baldyville

These are the conditions in Baldyville:

1. No two inhabitants have the same number of hairs on their head.
2. No inhabitant has exactly 518 hairs.
3. There are more inhabitants in town than hairs on any individual inhabitant's head.

What is the highest possible number of inhabitants?

## Unfaithful Wives

An anthropologist studying a primitive tribe in a remote location in the Amazon basin, had uncovered a strange tribal custom. Whereby, if a husband found out his wife was unfaithful to him, he must execute her in a public ceremony in front of the whole tribe on the same day at midnight. It so happened that every man in the tribe knew about every cheating wife except his own, since telling a man about his cheating wife was against the tribal honor code. On the day of his departure, the anthropologist held a tribal meeting and made the announcement: "I know there are unfaithful wives in this tribe." On the ninth day thereafter all cheating wives were executed at the same time.
How many unfaithful wives were there?

## Why 1 = 2

Find the mistake in these mathematical equations.
x = 2
x(x-1) = 2(x-1)
x2-x = 2x-2
x2-2x = x-2
x(x-2) = x-2
x = 1

## Open Polygon

Connect all 9 dots with 4 straight lines without lifting the pencil off the paper, and without going over the same line twice.