In this investigation you will
look at the moves a Knight
from a chess set might
make on a 100 square.
X
The knight
moves in an
L shape.
2 left or right and
1 up or down
X
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.
1
11
21
31
41
51
61
71
2
12
22
32
42
52
62
72
3
13
23
33
43
53
63
73
The knight starts on 35, where
4 5could
6 it 7be after
8 9 one
10move?
14 15 16 17 18 19 20
24 25 26 27 28 29 30
34 35 36 37 38 39 40
44 45 46 47 48 49 50
54 55 56 57 58 59 60
64 65 66 67Draw
68 all
69 the
70 possible
74 75 76 77answers
78 79 on
80your 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= 9
1+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
11=1+22+14-26
2= 1+12+25-37
12= 1+22+3-5
3= 1+22+3-24
13= 1+13-1
4=1+22+3-22
14= 1+13
5= 1+22-3-15
15= 1+22+14-22
6= 1+13+25-33
16= 1+22+14-26+5
7= 1+13+5+17-29
17= 1+13+5+17+9-28
8= -1-13+5+17
18= -1+22 -3
9= 1+22-14
19= 1+13+15
10= -1-22 +33
20= 1+22-3
If you were able to
complete this all your
squares will be filled in.
1
11
21
31
41
51
61
71
2
12
22
32
42
52
62
72
3
13
23
33
43
53
63
73
4
14
24
34
44
54
64
74
5
15
25
35
45
55
65
75
6
16
26
36
46
56
66
76
7
17
27
37
47
57
67
77
8
18
28
38
48
58
68
78
9
19
29
39
49
59
69
79
10
20
30
40
50
60
70
80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100