Do not be put off by long questions. Often the problem is easier the more information you are given at the start. Often too a long question helps to show the way through an intricate calculation. Short questions can be the hardest: ‘What is the formula of water?’ for a chemist; ‘Is this a question?’ for a philosopher.

Several of the problems have been used as examination questions. A few of these you may think entirely unreasonable to face under testing conditions, but remember that candidates would have had previous experience of these difficult topics in practical classes or tutorials.

The problems are more directed to number-crunching than to deduction. Partly this is the author's preference: you can't make valid deductions if you can't do the sums properly. Another reason for the bias is that deduction usually calls for some extra knowledge beyond the information that is given in the question. Not all readers of this book will have such knowledge.

Marking numerical questions isn't always as easy as you may imagine. If the answer is right, then OK, it is easy. Tracing where a wrong answer went wrong (which can take a lot of time) is necessary because the marker does want to give as much credit as possible when the candidate has got nearly everything right, but has made a slip near the end.