## Puzzles

Enjoy yourself trying to find the answers to these puzzles and games, some Mathematical, some just for fun. Please email This email address is being protected from spambots. You need JavaScript enabled to view it. if you need any help. Also if you have a puzzle to share, please email the details so we can include it here.

With each puzzle there are downloadable PDF files with solutions, if you need Adobe Acrobat Reader, please follow the link below

"... All the world is a laboratory to the inquiring mind..." (Martin H. Fischer)

Enjoy yourself trying to find the answers to these puzzles and games, some Mathematical, some just for fun. Please email This email address is being protected from spambots. You need JavaScript enabled to view it. if you need any help. Also if you have a puzzle to share, please email the details so we can include it here.

With each puzzle there are downloadable PDF files with solutions, if you need Adobe Acrobat Reader, please follow the link below

"... All the world is a laboratory to the inquiring mind..." (Martin H. Fischer)

### Braille investigation

A number puzzle based on Braille signs

Louis Braille developed a system of tactile reading for blind people.

It is based on a six dot pattern like the six on a die. Each Braille character is referred to as a cell.

Some of the Braille letters are shown below:-

Question. How many letters or Braille cells can you make with six dots?

**Investigation**

- Can you find out about more Braille letters?
- Are there any patterns in Braille?
- Are there any other reading systems for the blind?

Download the solution in PDF format

### Can You Add?

A little addition sum to try.

Can you add up the following?

Take 1000

Add 40 to it.

Now add another 1000.

Now add 30.

Add another 1000.

Now add 20.

Now add another 1000.

Now add 10.

What is the total?

IF YOU GOT 5,000 - TRY AGAIN!

### Chess Board

A number puzzle based on chess board

*"...I think therefore I am..." (Rene Descartes)*

How many squares are there on a standard chess board?

Clue: The answer isn't 64

### Coins in the Bank

A number puzzle with a hint of algebra

I have some money boxes and some £1 coins

If I put 7 coins into each money box I am left with 1 empty money box.

If I put 5 coins into each money box I am left with 1 coin.

How many money boxes and how many coins have I got?

Download the solution in PDF format

### Curve from straight lines

Just an interesting drawing

On a piece of graph paper, draw an x-y axis.

Mark divisions along the axis with small spaces - 1 or two of the smaller squares up to say 40.

Draw a straight line from 1 on the y axis to 40 on the x axis.

Draw another straight line from 2 on the y axis to 39 on the x axis.

Repeat the process.

Continue to process

You can make lots of different shapes by adding more curves.

### 8 Queens

This is the classic Sam Loyd puzzle from around 100 years ago.

The queen can move in any direction on a chess board, but only in a straight line.

Can you place queens on a chess board so that no queen can take one of the other queens?

Sam Loyd is famous for creating puzzles, he started off creating puzzles based on chess, but later created all types of puzzles.

You can download a PDF file with a chess board so you can work out your answer.

Sam Loyd maintained there were at least 12 different answers.

Download a chess board worksheet in PDF format

Download the solution in PDF format

### Fake Gold

A weighty logic puzzle that is a golden oldie!

A gold dealer is buying 27 gold bars, but he has been told one of the bars isn't gold and weighs less than a real gold bar.

He asks another trader if he can borrow his pan balance to check the gold bars. The trader allows him to use the scale, but says if he uses the scales more than three times, he has to give the trader half of the gold bars.

Can he find the fake bar by only using the scale three times?

Download the solution in PDF format

### 5 Card Trick

An ingenious but simple card trick

First, you have to make some cards, they can be any size, but making them similar to playing cards will make them easier to manage.

On the front of five cards, write the numbers 1 to 5 in black.

On the back of the cards, write the numbers 6 to 10 in red, 6 needs to be on the back of 1, 7 on the back of 2 etc

Hand the cards to a member of the audience and turn away from the audience.

Ask the member of the audience to drop the cards on the floor or table, in any pattern they like.

Ask them to tell you how many red cards they can see.

You can then tell them to total of the cards.

Can you work out how the trick works?

Download the solution in PDF format

### Four Two's

Can you make all the numbers between 1 and 100 using only four 2's, the four basic operations of: -

+, -, x, ÷

You can also use √ and ! (factorial) as well as anything mathematical such as sin, cos, tan etc.

The solution is 'work in progress'. If you have any contributions, please email them. We will credit the person who comes up with the answer first. Please indicate in the email if you would like your name credited. Email answers to This email address is being protected from spambots. You need JavaScript enabled to view it.

### Four Four's

A great number challenge that may take a little longer

you make all the numbers between 1 and 100 using only four 4's, the four basic operations of: -

+, -, x, ÷

You can also use √ and ! (factorial) as well as anything mathematical such as sin, cos, tan etc.

The solution is 'work in progress'. If you have any contributions, please email them. We will credit the person who comes up with the answer first.

Please indicate in the email if you would like your name credited. Email answers to This email address is being protected from spambots. You need JavaScript enabled to view it.

### For Lawn Gardener

Assistance required

A gardener has a lawn which is 72 m2 and the length and width are whole numbers.

He decides to change the shape of the lawn and make it 6 m longer and 2 m narrower, but he still wants the area to be 72 m2 and he still wants the length and width to be whole numbers.

Can you help to work out the new size of the lawn?

### fours_n_primes

A great prime number challenge that will take a little longer

Can you make all the prime numbers between 1 and 100 using only six 4's, the four basic operations of: -

+, -, x, ÷

You can also use √ and ! (factorial) as well as anything mathematical such as sin, cos, tan etc.

The solution is 'work in progress'. If you have any contributions, please email them. We will credit the person who comes up with the answer first. Please indicate in the email if you woudl like your name credited. Email answers to This email address is being protected from spambots. You need JavaScript enabled to view it. "> This email address is being protected from spambots. You need JavaScript enabled to view it.

### Konigsberg Bridge Problem

help needed!

One of the residents of Konigsberg wants to walk around the town and cross each of the seven bridges once. He also wants to finish his walk at the same place he started.

Can you work out a route?

### Lazy Gardener

A little logic puzzle

It takes two gardeners 8 days to mow a field.

One gardener is lazy and one is energetic.

The energetic one would only take 12 days to mow it on his own.

How many days would the lazy gardener take to mow the field on his own?

### Measuring Liquid problem

A little logic puzzle

You need to measure out 4 litres of water

You have an unlimited supply of water, and two measuring jugs, one 3 litre and one 5 litre.

Can you work out how to get 4 litres?

### Mind Reading Cards

A card trick to baffle your friends

Take 21 playing cards and lay them out in 3 columns of 7. Place the cards so that each card covers part of the card below as this will make it easier to collect them later.

Ask someone to choose a card and tell you which column it is in, but not to tell you the card.

Gather the cards into three piles, making sure you keep them in order.

Place the pile with the chosen card in between the other two piles.

Lay the cards out again in the same way, putting them down in rows of three.

Ask the person to say which column the card is in.

Gather them up again making sure the pile with the chosen card is in between the other two piles.

Lay the cards out again, in rows of three.

Ask the person the say which column their card is in.

Gather the cards up for the final time, again keeping them in order, and placing the pile with the chosen card in between the other two piles.

Fan out the cards and without giving the trick away, select the 11th card. This is the chosen card.

You can also use 15 cards or 27 cards rather than 21. The trick is the same, only the position of the chosen card changes. With 15 cards it is the 8th card and with 27 cards it is the 14th.

Download the solution in PDF format

### Mystic Number

A number trick to amaze your friends

On a piece of paper, write the number 1089 and fold the paper so nobody (including you) can see it, and give it to someone in the audience to hold.

Ask another person in the audience to write down a three digit number, any number they choose, the only thing is the first and last digits must be different.

Ask them to reverse the digits and subtract the smaller number from the larger. Reverse the digits in the answer adding a zero if there are only two in the answer.

Now add these two numbers together. Your audience will be astounded when you unfold the piece of paper to show the same number. This works with any three digit number providing the first and last digits are different.

Below is a worked example.

Choose a number, say 721, reverse the digits 127

721 subtract 127 = 594

594 reverse the digits 495

594 plus 495 = 1089

Try it with other numbers

If you want to make it more impressive, instead of writing down the answer, get a telephone directory and look on page 108 and find the 9th entry and write this down instead. When you are given the answer, ask one of the audience to look at the phone book and read out the 9th name on page 108. They will be amazed at your mind-reading powers.

"...I'm pink therefore I'm spam..." (Anon)

### Painted Cube

### A 3-D spacial puzzle

A 3cm x 3cm x 3cm wooden cube is painted red. When the paint is dry, it is cut into 1cm x 1cm x 1cm cubes. How many of the 1cm cubes have all 6 faces painted red, how many with 5, 4 etc.? Can you find a formula in terms of an n-sided cube? Test your formula with other cubes.

Download the solution in PDF format

### Prime Factors

A prime number brain teaser

Numbers can be written as the product of other numbers. For example, 12 can be written as 2 x 6 or 3 x 4. You can also write a number as the product of prime factors.

Using 12 again, we can write this as 2^{2} x 3.

There are several ways of working out the prime factors, one way is as follows:-

If we take 72 as our example. The first step is to start 2 and see if it can be divided by 2. As 72 is even we can divide by 2.

So we can write 2 x 36 and we can then divide 36 by 2 so we have

2 x 2 x 18 and again we can divide 18 by 2 so we have 2 x 2 x 2 x 9.

We can't divide 9 by 2 so we now look at the next prime number 3 and 9 can be written as 3 x 3 so we now have: -

2 x 2 x 2 x 3 x 3

We can then tidy this up by writing it as 2^{3} x 3^{2}

Can you write all of the numbers from 2 to 100 as prime factors?

### River Crossing

A logic brain teaser

A farmer has

a chicken | a fox | and a sack of grain |

which he needs to take across the river. His boat can only carry the farmer and 1 item at a time.

If he takes the grain, the fox will eat the chicken and if he takes the fox, the chicken will eat the grain.

Can you work out how the farmer can cross the river without losing anything?

Download the solution in PDF format

"... Elementary tables are made from logs with square roots..." (Anon)

### Sheep Pens

### A rustic brain teaser!

A farmer has some sheep and some sheep pens. If he puts 5 sheep in a pen he has an empty pen. If he puts 4 sheep in a pen he has 1 sheep left over.

How many sheep and how many pens does the farmer have?

NO SHEEP WERE HARMED IN THE MAKING OF THIS PUZZLE!

### Sieve of Eratosthenes

A fun way to find prime numbers

Eratosthenes was a Greek mathematician who developed various theories about prime numbers.

Starting at 2, colour in every second square, leaving 2 itself blank. Now from 3 and using a different colour, shade in every third square.

Repeat this process until you can't do any more. The un-shaded numbers are the prime numbers up to 200.

You can download a worksheet to find all the prime numbers up to 200, click the link below the grid.

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 60 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 |

111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 |

121 | 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 | 130 |

131 | 132 | 133 | 134 | 135 | 136 | 137 | 138 | 139 | 140 |

141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 |

151 | 152 | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 |

161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 160 |

171 | 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 |

181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 |

191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 |

Download the worksheet in PDF format

Download the solution in PDF format

### Two Numbers

A simple algebraic puzzle

### White Knuckle Ride

Another algebra puzzle

The total fare for 2 adults and 3 children on the Chuck-A-Bucket ride is £14.00.

If a child's fare is one half of an adult's fare, what is the adult fare?

Download the solution in PDF format