Introduction |
xiii |
Part 1: Short investigations |
1 |
Advice to the reader |
2 |
|
1 Analysing games |
3 |
1.1 Introduction |
3 |
1.2 First short investigation |
5 |
1.3 Further problems |
8 |
1.4 Solutions to exercises in 1.2 |
10 |
|
2 From rhyme to reason |
12 |
2.1 Introduction |
12 |
2.2 Second short investigation |
12 |
2.3 Further problems |
16 |
2.4 Solutions to exercises in 2.2 |
21 |
|
3 Thinking things through |
23 |
3.1 Introduction |
23 |
3.2 Third short investigation |
24 |
3.3 Further problems |
29 |
3.4 Solutions to exercises in 3.2 |
31 |
|
4 Asking questions |
35 |
4.1 Introduction |
35 |
4.2 Fourth short investigation |
36 |
4.3 Further problems |
47 |
4.4 Solutions to exercises in 4.2 |
51 |
|
Part 2: Extended investigations |
55 |
Advice to the reader |
57 |
Investigation I: Flips |
61 |
5 Introducing 9-flips |
63 |
Solutions |
68 |
6 The art of guessing |
69 |
Solutions |
75 |
7 Other flips |
77 |
Solutions |
80 |
8 Flips in other bases |
83 |
Solutions |
85 |
9 Counting 9-flips with n digits |
88 |
Solutions |
101 |
10 Recurrence relations |
103 |
Solutions |
111 |
11 The end of the road |
113 |
Solutions |
115 |
Postscript |
117 |
Investigation II: The postage stamp problem |
119 |
12 Getting stuck in |
121 |
Solutions |
125 |
13 Coming unstuck: the search for proof |
127 |
Solutions |
132 |
14 One picture is worth a thousand words |
136 |
Solutions |
147 |
15 The final licking |
152 |
Solutions |
159 |
16 The coin problem |
162 |
Solutions |
165 |
Postscript |
167 |
Solutions |
169 |
|
17 Further problems for extended investigation |
172 |
17.1 Introduction |
172 |
17.2 Further problems |
175 |
17.3 Outlines and hints |
176 |
Index |
205 |