### 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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## Guilders Expense Riddle

While building a medieval cathedral, it cost 37 guilders to hire 4 artists and 3 stonemasons or 33 guilders for 3 artists and 4 stonemasons. What would the expense of just one of each?

Hint:

Ten guilders. An artist cost 7 guilders, and a stonemason cost 3 guilders.

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## Shotgun Pete Riddle

Shotgun Pete owned a lot of guns. He left a quarter of them in Death Valley, gave one to each of the three passengers in the stagecoach, and kept half of them with him. How many guns did Pete own?

Hint:

## One Third As Old Riddle

Hint:

## Add Up To 100 Riddle

With the numbers 123456789, make them add up to 100. They must stay in the same order. You can use addition, subtraction, multiplication, and division. Remember, they have to stay in the same order!

Hint:

## How Many Spaces Riddle

Hint:

64; the space that comes after the 64th spoke, would be the first spoke.

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## 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.

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## 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.

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## 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.

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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

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