### Fun Facts (Hints)

Mathematics has an extensive history in just about every culture or civilized society known to man. Listed below are some cool facts to get those math juices flowing:
In 1852 mathematician JJ Sylvester established the "theory of algebraic invariants."
In 1995 math great Andrew Wiles, proved "Fermat's Last Theorem."
The first decimal number system is said to have been invented in Ancient Egypt around 5000BC.
The Ancient Mayan civilization located in Central America is one of the only cultures in the recorded history of the world to use a place-value number system.
The American Mathematical Society was formed in the late months of 1888 in New York.

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Riddles and Answers © 2023

## The Bus Stop Riddle

An empty bus pulls up at a stop and 5 people get on. At the next stop 5 people get off and twice as many people get on as at the first stop. At the third stop 10 people get off.

How many people are on the bus at this point?

How many people are on the bus at this point?

Hint:

Ne, the bus driver.

On the 1st stop, 5 people get on. On the 2nd stop, 5 people get off and 10 (twice as many as at 1st stop) people get on. On the 3rd stop, 10 people get off. So there are (5 5 + 10 10) 0 passengers left, which leaves the bus driver as the only person on board the bus.

YES NO

On the 1st stop, 5 people get on. On the 2nd stop, 5 people get off and 10 (twice as many as at 1st stop) people get on. On the 3rd stop, 10 people get off. So there are (5 5 + 10 10) 0 passengers left, which leaves the bus driver as the only person on board the bus.

*Did you answer this riddle correctly?*YES NO

## Three Rivers Riddle

There are three rivers and after each river lies a grave. A man wants to leave the same number of flowers at each grave and be left with none at the end. However, each time he passes through a river, the number of flowers he has doubles. How many flowers does he have to start with so that he is left with none at the end? And how many does he leave at each grave?

Hint:

This problem has an infinite number of solutions modeled by the equation 8a=7n, where a is the amount of flowers the man starts with and n is the number of flowers he leaves at each grave. The simplest and possibly trivial solution would be to start with 0 flowers and leave 0 flowers at each grave. A more significant solution would be to start with 7 flowers and leave 8 at each grave. Any positive integer multiple of this solution also satisfies the conditions. For example, the man starts with 14 flowers and leaves 16 at each grave; so, 14 doubles to 28, and 28-16= 12; 12 doubles to 24, and 24-16= 8; 8 doubles to 16, and 16-16= 0. The result is the same if the man starts with 21 flowers and leaves 24 flowers at each grave, or starts with 28 and leaves 32.

YES NO

*Did you answer this riddle correctly?*YES NO

## Farmer Stones Riddle

A farmer had a stone that he used to measure grain on his scale. One day his neighbor borrowed the stone, and when he returned, it was broken into four pieces. The neighbor was very apologetic, but the farmer thanked the neighbor for doing him a big favor. The farmer said that now he can measure his grain in one pound increments starting at one pound all the way to forty pounds (1, 2, 3, 17, 29, 37, etc.) using these four stones.

How much do the four stones weight?

How much do the four stones weight?

Hint:

The stones weight 1 pound, 3 pounds, 9 pounds and 27 pounds. These can be used in combination with each other on both sides of the scale to come up with any counterweight from 1 to 40 pounds.

YES NO

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## A Farmers Sheep Riddle

Hint:

## How Many Chocolates Can You Get?

A shop sells 1 chocolate at $1. You can exchange 3 wrappers for 1 chocolate. If you have $15, how many chocolates can you get?

Hint:

15 chocolates with resale. 15 then with 15 wrappers you get 5 more chocolates. With 3 wrappers from the 5 new chocolates you get 1 more chocolate. And with these 1 more wrapper and the remaining 2 wrappers you get 1 more chocolate. Hence you get total 15 + 5 + 1 + 1 = 22

YES NO

*Did you answer this riddle correctly?*YES NO

## The Jacksons Wedding Day Riddle

When the Jacksons married 18 years ago, Mr. Jackson was three times as old as his wife, and today he is just twice as old as she?

How old was Mrs. Jackson on the wedding day?

How old was Mrs. Jackson on the wedding day?

Hint:

Mr. Jackson was 54 and his wife was 18. Now hes 72 and his wife 36.

YES NO

*Did you answer this riddle correctly?*YES NO

## Two Girls On A Train

Two schoolgirls were traveling from the city to a dacha (summer cottage) on an electric train.

"I notice," one of the girls said "that the dacha trains coming in the opposite direction passes us every 5 minutes. What do you think-how many dacha trains arrive in the city in an hour, given equal speeds in both directions?"

"Twelve, of course," the other girl answered, "because 60 divided by 5 equals 12."

The first girl did not agree. What do you think?

"I notice," one of the girls said "that the dacha trains coming in the opposite direction passes us every 5 minutes. What do you think-how many dacha trains arrive in the city in an hour, given equal speeds in both directions?"

"Twelve, of course," the other girl answered, "because 60 divided by 5 equals 12."

The first girl did not agree. What do you think?

Hint:

If the girls had been on a standing train, the first girl's calculations would have been correct, but their train was moving. It took 5 minutes to meet a second train, but then it took the second train 5 more minutes to reach where the girls met the first train. So the time between trains is 10 minutes, not 5, and only 6 trains per hour arrive in the city.

YES NO

*Did you answer this riddle correctly?*YES NO

## Outrunning A Train Riddle

Walking home one day, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and jump off the track as the train is about to run you down. As it happens, if you had gone the other way, you would have reached safety just before being run over as well. If you can run ten miles per hour, how fast is the train moving?

Hint:

The train is moving at 40 miles per hour. Imagine that a friend is walking with you. When the train whistle blows, you head away from the train, he heads toward it. When he reaches safety, you will be 6/8 (or 3/4)of the way across the bridge, and the train will have just reached the bridge. For the train to cross 4/4 of the bridge in the time you cross the remaining 1/4, the train must be moving four times your speed.

YES NO

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## Three Sides And Three Angles

I have 3 sides. I have 3 angles. I have 3 vertices. I can be equilateral, isosceles, or scalene. What 2D shape am I?

Hint:

## Brothers And Sisters Riddle

My daughter has as many sisters as she has brothers. Each of her brothers has twice as many sisters as brothers. How many sons and daughters do I have?

Hint:

Four daughters and three sons. Each daughter has 3 sisters and 3 brothers, and each brother has 2 brothers and 4 sisters.

To figure it out mathematically, you could use the following two equations where G = the number of girls and B = the number of boys:

G 1 = B

2(B 1) = G

Solving for G gives you 4 and plugging that in to G 1 = B gives you a B of 3.

YES NO

To figure it out mathematically, you could use the following two equations where G = the number of girls and B = the number of boys:

G 1 = B

2(B 1) = G

Solving for G gives you 4 and plugging that in to G 1 = B gives you a B of 3.

*Did you answer this riddle correctly?*YES NO

## The Magic Number Riddle

Think of a number

Multiply times 2

Add 6

Divide by 2

Subtract the first number you thought of

What is the number you came up with?

Multiply times 2

Add 6

Divide by 2

Subtract the first number you thought of

What is the number you came up with?

Hint:

The answer is 3

If you got a different number you did the math wrong

YES NO

If you got a different number you did the math wrong

*Did you answer this riddle correctly?*YES NO

## Owls And Wolves Riddle

You are in the woods with owls and wolves. There are 22 eyes and 32 legs. How many owls and wolves are there?

Hint:

5 owls and 5 wolves, (not 6 owls because 2 of the eyes and legs are yours).

2 * owls + 2 * wolves = 20 eyes

2 * owls + 4 * wolves = 30 legs

owls + wolves = 10 eyes owls = 10 wolves

owls + 2 * wolves = 15 10 wolves + 2 * wolves = 15 wolves = 5

owls + 5 = 10 owls = 5

YES NO

2 * owls + 2 * wolves = 20 eyes

2 * owls + 4 * wolves = 30 legs

owls + wolves = 10 eyes owls = 10 wolves

owls + 2 * wolves = 15 10 wolves + 2 * wolves = 15 wolves = 5

owls + 5 = 10 owls = 5

*Did you answer this riddle correctly?*YES NO

## Lakes And Boats Riddle

There is a lake with shores A and B. Two motorboats M and N are standing on the opposite sides (A and B respectively). M leaves A and N leaves B and start moving with constant speeds. They meet for the first time 500 yards away from A. After touching the shores, they return back to the previous shore point without taking any break. This time they meet at 300 yards away from B.

Can you determine how wide the lake is? What is the relation between the speeds of boats?

Can you determine how wide the lake is? What is the relation between the speeds of boats?

Hint:

When the boats meet for the first time, they have sailed a combined distance that is equal to one length of the lake. When they meet the second time, they have sailed 3 lengths. The elapsed time and the distance for each is three times.

When they meet for the second time, the boat M has sailed 500 x 3 = 1500 yards. Now, this is 300 yards longer than the length of the lake, it must be 1200 yards wide.

The ration between the speed of boat M and boat N is equal to the ratio of the distance that they have sailed before they meet the first time.

YES NO

When they meet for the second time, the boat M has sailed 500 x 3 = 1500 yards. Now, this is 300 yards longer than the length of the lake, it must be 1200 yards wide.

The ration between the speed of boat M and boat N is equal to the ratio of the distance that they have sailed before they meet the first time.

*Did you answer this riddle correctly?*YES NO

## Sand Piles Riddle

A child playing on the beach had 6-1/6 sand piles in one place and 3-1/3 in another. If he put them together, how many sand piles would he have?

Hint:

## Eight Balls

There are eight balls, one of which is slightly heavier than the others. You have a two-armed scale, which you are allowed to use only twice. Find the ball thats heavier.

Hint:

Put three balls on each side of the scale. If the arms are equal, you know the heavy ball is one of the two remaining. If the arms are unequal, take the three balls on the heavier side, pick two and weigh them against each other.

YES NO

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## Post Your Math Brain Teasers Below

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