In this investigation you will look at the moves a Knight

from a chess set might make on a 100 square.

X

X

The knight moves in

an L shape.

2 left or right and 1 up or down

Or

1 left or right and 2 up or down

From this starting position the knight could

move to each of the squares

marked with a circle.

80797877767574737271

70696867666564636261

60595857565554535251

50494847464544434241

40393837363534333231

30292827262524232221

20191817161514131211

10987654321

The knight starts on 35, where could it be after one

move?

Draw all the possible answers on your 100

square.

The Century Knight wants to get to the 100 square.

Your task is to plot the journey from 1 to 100 in

the fewest number of moves.

1) Break the problem into smaller pieces

2) Tabulate results

3) Look for patterns and why they occur

4) Find a formula

5) Solve the problem

Route taken(squares landed on)

Number of moves

The Century Knight wants to get to the 100 square.

Your task is to plot the journey from 1 to 100 in the fewest number of moves.

The minimum number of moves is 6

One such route is 13, 25, 37, 58, 79,100

Do you have another?

The Square Knight has to see all the square numbers.

Plot a journey that visits every square number.

Is this possible?What is the shortest path?

The Cube Knight has only the cube numbers to inspect.

Plot a journey that visits all the cube numbers up to 100, starting from 1.

Is this possible?What is the shortest path?

What is the shortest path if you visit them in ascending order.

The Target Knight combines the numbers from each square it visits

using addition or subtraction.For example:

1+22-14= 91+13-1 = 12

Your task is to find ways of making all the numbers 1 to 20.

Your task is to plot a journey starting from 1 that visit every number up to

100.

Is this possible?

The Square Knight has to see all the square numbers.

One possible journey is

1, 13, 25, 4, 16, 28, 9, 30, 49, 57, 36, 44, 56, 64, 83, 62, 81, 73, 85,

77,98, 79, 100

The Cube Knight has only the cube numbers to inspect.

Plot a journey that visits all the cube numbers up to 100, starting from 1.

A 10 move journey: 1,13, 25, 6, 27, 8, 16, 24, 45, 64

Or in ascending order:

1,13, 5, 17, 29, 8, 27, 35, 56, 64

This is also 10 moves.

1= 1

2= 1+12+25-37

3= 1+22+3-24

4=1+22+3-22

5= 1+22-3-15

6= 1+13+25-33

7= 1+13+5+17-29

8= -1-13+5+17

9= 1+22-14

10= -1-22 +33

11=1+22+14-26

12= 1+22+3-5

13= 1+13-1

14= 1+13

15= 1+22+14-22

16= 1+22+14-26+5

17= 1+13+5+17+9-28

18= -1+22 -3

19= 1+13+15

20= 1+22-3

If you were able to complete this all your

squares will be filled in.

100999897969594939291

70696867666564636261

60595857565554535251

50494847464544434241

40393837363534333231

30292827262524232221

20191817161514131211

10987654321

797877767574737271

898887868584838281 90

80