### 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 © 2021

## 150 Pens Riddle

Rihanna brought home 150 pens but while packing them, she misplaced some of them. When her brother asked how many she had misplaced, she told him:

If you count in pairs, one will remain

If you count in a group of three, two will remain

If you count in a group of four, three will remain

If you count in a group of five, four will remain

If you count in a group of six, five will remain

If you count in a group of seven, nothing will remain.

How many pens do you think has she misplaced ?

If you count in pairs, one will remain

If you count in a group of three, two will remain

If you count in a group of four, three will remain

If you count in a group of five, four will remain

If you count in a group of six, five will remain

If you count in a group of seven, nothing will remain.

How many pens do you think has she misplaced ?

Hint:

## The Jug Full Of Beer

A barman is having a 12 liters jug full of beer. He needs to divide or split that beer into two equal parts. All he has is two empty jugs of capacity 8 liters and 5 liters.

How will he do it using them?

How will he do it using them?

Hint:

First fill the 8 liters jug complete - 4, 8, 0

Fill the 5 liters jug with 8 liters jug - 4, 3, 5

Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0

Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3

Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3

Fill the 5 liters jug from the 8 liters jug - 1, 6, 5

Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.

YES NO

Fill the 5 liters jug with 8 liters jug - 4, 3, 5

Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0

Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3

Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3

Fill the 5 liters jug from the 8 liters jug - 1, 6, 5

Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.

*Did you answer this riddle correctly?*YES NO

## A Large Box Of Money Riddle

I have a large money box, 48 centemeters square and 42 centemeters tall. Roughly how many coins can I place in my empty money box?

Hint:

## Filling Your Buckets Riddle

You have a 5 gallon bucket and a 3 gallon bucket with as much water as you need, but no other measuring devices. Fill the 5 gallon bucket with exactly 4 gallons of water.

Hint:

Fill the 5 gallon bucket all the way up. Pour it into the 3 gallon bucket until it is full. Empty the 3 gallon bucket. Pour the remaining 2 gallons into the 3 gallon bucket. Fill the 5 gallon bucket all the way up. Finish filling the 3 gallon bucket.

YES NO

*Did you answer this riddle correctly?*YES NO

## Feet In A Yard Riddle

Hint:

## Making Ten Riddle

Hint:

Yes it is possible in Roman Numerals. In Roman Numerals,

9 = IX

10 = X

11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.

YES NO

9 = IX

10 = X

11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.

*Did you answer this riddle correctly?*YES NO

## Zebras And Ostriches In The Zoo

There are zebras and ostriches in this Zoo.

You count 80 heads and 200 legs.

Can you find the number of Zebras and the number of Ostriches in the Zoo?

You count 80 heads and 200 legs.

Can you find the number of Zebras and the number of Ostriches in the Zoo?

Hint:

The number of Ostriches = 60 & The number of Zebras = 20

YES NO

*Did you answer this riddle correctly?*YES NO

## The Greater Dozen Riddle

Hint:

## A Rickety Bridge Riddle

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

Hint:

17 mins.

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross

2 comes back

7 and 10 go across

1 comes back

1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

YES NO

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross

2 comes back

7 and 10 go across

1 comes back

1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

*Did you answer this riddle correctly?*YES NO

## Seventeen Apples Riddle

Hint:

## 10 Boxes Riddle

There are ten boxes containing some balls. Each of the ball weighs exactly 10 grams. One of those boxes have defective balls (all the defective balls weigh 9 grams each).

An electronic weighing machine is provided to you and you are allowed only one chance of weighing on it.

How will you find out which box has defective balls ?

An electronic weighing machine is provided to you and you are allowed only one chance of weighing on it.

How will you find out which box has defective balls ?

Hint:

Let us simplify boxes by naming them from 1 to 10.

Now the trick here is to pick different number of balls from different boxes. So to simplify things, we will pick balls corresponding to box number.

Thus, pick 1 ball from Box 1, 2 balls from box 2, 3 balls from box 3 and so on. You will have 55 balls altogether. Now, put them all in the balance.

If all balls were weighing accurate 10 grams, the total weight of the 55 balls would have been 550 grams. But one of the box must have had the defective balls.

Suppose if the defective balls were in box number 2, then the total weight will be 2 grams less than 550. If the defective balls were in box 8, the total weight will be less than 8 grams from 550. In this way, you will be able to identify which box has the defective balls.

YES NO

Now the trick here is to pick different number of balls from different boxes. So to simplify things, we will pick balls corresponding to box number.

Thus, pick 1 ball from Box 1, 2 balls from box 2, 3 balls from box 3 and so on. You will have 55 balls altogether. Now, put them all in the balance.

If all balls were weighing accurate 10 grams, the total weight of the 55 balls would have been 550 grams. But one of the box must have had the defective balls.

Suppose if the defective balls were in box number 2, then the total weight will be 2 grams less than 550. If the defective balls were in box 8, the total weight will be less than 8 grams from 550. In this way, you will be able to identify which box has the defective balls.

*Did you answer this riddle correctly?*YES NO

## Eating Burgers Riddle

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours ?

How many burgers can 9 boys eat in 3 hours ?

Hint:

18

More hours => more burgers.

More boys => more burgers.

The time become twice (3 hours / 1.5 hours).

Boys become six times (9 / 1.5).

Number of burgers = 2 * 6 * Original(1.5)

= 18

YES NO

More hours => more burgers.

More boys => more burgers.

The time become twice (3 hours / 1.5 hours).

Boys become six times (9 / 1.5).

Number of burgers = 2 * 6 * Original(1.5)

= 18

*Did you answer this riddle correctly?*YES NO

## Bigger Upside Down Riddle

Hint:

## Adding Eights Riddle

Hint:

## Green And Red Apple Trees Riddle

One of the apple trees had only green apples, and the other tree had only red apples. The village boys picked all the apples from both trees, and found that there were 5 red apples for every 4 green apples. Between them, the boys then ate 16 red apples and 16 green applies. When they counted the apples that were left, they found there were 3 red apples for every 2 green apples. How many apples of each color were on the trees in the first place?

Hint:

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