THE CRYSTAL MAZE

Get into teams of 4

The Crystal Maze is split into four zones based on four ancient cultures that made important Mathematical discoveries

Each zone has three puzzles:A physical puzzle that requires you to make something

A skill puzzle that uses some of the number skills you have learntA mystery puzzle - something slightly different to the usual!

3 crystals are awarded to the team that finishes first2 crystals are awarded to the team that finishes second1 crystal is awarded to the team that finishes third

For each puzzle:

Each crystal counts as a 5 second head-start on a final puzzle to be revealed after the rest...

GREEK EGYPTIAN

INDIAN CHINESE

physical skill mystery

Plato is best known for his identification of 5 regular solids now known as the Platonic Solids, made from one regular shape each:

Tetrahedron

Cube

Dodecahedron

Use the straws and play doh to make an icosahedron (hint – it has 20 sides)

Octahedron

Icosahedron

Euclid is known as the ‘father of geometry’ and laid down the rules of geometry still used today. He also wrote about primes and proved that there an infinite number of them...

Take the first n primes, multiply them together and add one to obtain a new prime.

Eg using the first 3 primes 2,3 and 5

2 x 3 x 5 = 30

30 + 1 = 31 is prime

Without a calculator, evaluate the prime given by this method, using the first 8 primes

1191713117532 = 9699691

The Greeks knew of several rules for the area of a triangle.

215134 s 16 131216 Area

576

csbsass 2cbas Area = where a b

c

Find the area of a triangle with sides of 4, 13 and 15cm

24

Hero worked out this formula for a triangle with sides a, b and c

physical skill mystery

Egyptians realised that the volume of a pyramid is a third of the volume of a cuboid with the same base and height

2

2

3

volume of cuboid = 2 x 2 x 3 = 12

Cut out the nets, fold and stick to make 3 pyramids.Then fit all 3 together to

make a cube!

so volume of pyramid = 4

Eg

The Egyptians liked to keep things simple

Eg 31

21

They only liked to use unit fractions - with one for the numerator.

65

Eg 81

41 8

3

can be written two ways as an Egyptian fraction:

81

61

247

247

41

121

247

101

601 12

1301 15

1201

Find three ways to write as an Egyptian fraction760

Egyptians used symbols to represent numbers:

Solve this problem, giving your answer in the Egyptian style!

52431572 26205524

physical skill mystery

Indian mathematicians were the first to develop the concepts of zero and negative numbers

5

1-

6

05-

Cut out and position the numbers so that every circle add up to zero

-3 2 7

-4 -2 3

-6 1 4

Use 8 8s in an addition sum to make 1000

888 + 88 + 8 + 8 + 8

Indian mathematicians were the first to develop a proper decimal system

Indian Mathematicians knew how to quickly add up difficult-looking sums like 333333 10099...4321

Possibly related, how many squares can be fitted into the grid?

(the answer is 25502500 by the way)

22222 54321

5 x 5 ways to fit a 1 by 1 square

4 x 4 ways to fit a 2 by 2 square

3 x 3 ways to fit a 3 by 3 square

2 x 2 ways to fit a 4 by 4 square

1 x 1 way to fit a 5 by 5 square

= 55 squares

There are:

physical skill mystery

Tangrams are an ancient Chinese puzzleStarting with a square made up of 7 pieces…you must arrange them to make something else

Cut and rearrange the square to make a parallelogram

Chinese mathematicians found ways to deal with many problems at once

52 is the first number in all 3 lists

I have a bag of sweets

If I share them between 5 people there are two sweets left over

If I share them between 7 people there are three sweets left over

If I share them between 3 people there is one sweet left over

What is the least number of sweets in the bag?

Could be 4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,...

Could be 10, 17, 24, 31, 38, 45, 52, 59, ...

Could be 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, ...

Chinese Mathematicians were intrigued by magic shapes...

Use the digits 1 to 9 to make a magic triangle where each side adds to 23

Magic squares

Any line of 3 adds to the same total

Magic circles

Any diameter or circle adds to the same total

Magic triangles

Any side adds to the same total

7

89

6

251

34

7

89

5

324

61

or

5

1-

6

05-

-3 2 7

-4 -2 3

-6 1 4

1 2 3

4 5 6

7 98

GreekPhysical

Skill 9699691

Mystery 24

EgyptianPhysical

Skill

Mystery

101

601 12

1301 15

1201

PhysicalIndian

Skill 888+88+8+8+8Mystery 55

ChinesePhysical

Skill 52

Mystery

Solutions

Final challenge