Consider the following number trick–try it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers). Then against 2 they write the sum of the entries against 0 and 1; against 3 they write the sum of the entries against 1 and 2; and so on. Once they have completed the process, producing entries against each number from 0 to 9, you suggest that, as a check, they call out the entry against the number 6. Thus their table (which, of course, you do not see) might look like the table in the margin. You now ask them to add all the entries in the second column, while you write 341 quickly on a slip of paper.