 The combined area of these three shapes is approximately 15.57 squares. Archimedes showed that the surface area and volume of a sphere is exactly 2/3 of the area and volume of the surrounding cylindrical surface.

# Mathematic puzzles

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules as do multiplayer games, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. (Wikipedia)

Easier puzzle

## Round or square?

If the price is the same, would you prefer to have a 10-inch round pizza or a 9-inch square pizza?

The area of 9-inch pizza is 9x9 = 81 square inches
and the area of a 10-inch round pizza is πR² = 3.1416 x (10/2)² = 78.54 square inches.

Reference: Wikipedia Area

Algebra puzzle

## How fast should you drive?

When you drive to work at 60mph, you arrive there early. When you drive at 30 mph, you arrive late. The amount of time you are early is the same as the amount of time you're late. How fast should you drive so that you can be on time ?

Answer: You should drive at 40 mph to be right on time.

Let the distance = D

If you drive at 60 mph, it will take D/60 hours to arrive,
If you drive at 30 mph, it will take D/30 hours to arrive,
If you drive at x mph to be on time, it will take D/x hours to arrive,

D/x should be the average of D/60 and D/30.

All you need is to solve this equation:   D/x = ( D/60 + D/30 )/2

You will find that  x = 40

Algebra puzzle

## Can 2=1 ?

If A=B
Multiply by A on both sides, you get A²=AB.
Subtract B² from both sides, you get A²-B²=AB-B².
Factor both sides, you get (A+B)(A-B)=B(A-B).
Divide by (A-B) on both sides, you get A+B=B.
Because A=B, therefore B+B=B,
If 2B=B, then 2=1.

Answer: The problem is when you try to divide both sides by (A-B). Because A=B, therefore (A-B)=0. You can't divide any equation by zero.

Easier puzzle

## Round or square?

If the price is the same, would you prefer to have a 10-inch round pizza or a 9-inch square pizza ?

The area of 9-inch pizza is 9x9 = 81 square inches
and the area of a 10-inch round pizza is πR² = 3.1416 x (10/2)² = 78.54 square inches.

Reference: Wikipedia Area

Algebra puzzle

## How much does a brick and a half weigh ?

If a brick weighs 3 pounds plus half a brick, how much does a brick and a half weigh?

Answer: You might be able to figure out the result without fancy mathematics, but it is a better to use a simple algebra.

Let the weight of the brick = X pounds
X = 3 + X/2
X - X/2 = 3
X/2 = 3
X = 6    Therefore a brick weighs 6 pounds.
So a brick and a half must weight 9 pounds.

Algebra puzzle

## I spent half of my money

I went to a store and spent half of my money. I now have as many pennies(cents) as I had dollars before and half as many dollars as I had pennies before. How much do I have now?

Answer: I started with \$99.98. I spent \$49.99 and now have \$49.99.
I now have 99 cents as I had 99 dollars before.
I now have 49 dollars which is half as 98 cents before.

See if you can use algebra to solve this problem.

## Mathematic puzzle

This Math Problem Will Make You Question Everything You Ever Knew About Algebra. The question originally went viral in Japan, after a study discovered that only 60 percent of 20-somethings could actually solve it.
If you arrived at 3, 7, or 9 as your answer, you're wrong.
As you can see, not even a calculator can help you, as it will read the problem wrong and arrive at the answer of 9. To solve it correctly in a calculator, you need to write it out like this: 9-3/(1/3) + 1, which will lead you to 1 as the correct answer.

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