In this investigation you will look at the moves a Knight from a chess set might make on a 100 square.

1
The Knight's Move

• In this investigation you will look at the moves
  a Knight from a chess set might make on a 100
  square.

2
The Knight's Move
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
3
The Knight's Move
From this starting position the knight could move
to each of the squares marked with a circle.
4
The Knight's Move
The knight starts on 35, where could it be after
one move?
Draw all the possible answers on your 100 square.
5
The Century Crusade

• 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.

6
Strategy
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
7
Tabulate your results
Route taken (squares landed on) Number of moves





8
The Century Crusade

• 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?
9
The Square Crusade

• 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?

10
The Cube Crusade

• 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.

11
The Target Crusade

• The Target Knight combines the numbers from each
  square it visits using addition or subtraction.
• For example
• 122-14 9
• 113-1 12
• Your task is to find ways of making all the
  numbers 1 to 20.

12
The Complete Crusade

• Your task is to plot a journey starting from 1
  that visit every number up to 100.
• Is this possible?

13
The Square Crusade

• 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
14
The Cube Crusade

• 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.
15
The Target Crusade
1 1 2 11225-37 3 1223-24 41223-22 5
122-3-15 6 11325-33 7 113517-29 8
-1-13517 9 122-14 10 -1-22 33

• 1112214-26
• 12 1223-5
• 13 113-1
• 14 113
• 15 12214-22
• 16 12214-265
• 17 1135179-28
• 18 -122 -3
• 19 11315
• 20 122-3

16
The Complete Crusade

• If you were able to complete this all your
  squares will be filled in.

17
The Knight's Move
10
9
8
7
6
5
4
3
2
1
20
19
18
17
16
15
14
13
12
11
30
29
28
27
26
25
24
23
22
21
40
39
38
37
36
35
34
33
32
31
50
49
48
47
46
45
44
43
42
41
60
59
58
57
56
55
54
53
52
51
70
69
68
67
66
65
64
63
62
61
79
78
77
76
75
74
73
72
71
80
89
88
87
86
85
84
83
82
81
90
100
99
98
97
96
95
94
93
92
91
18
The Knight's Move