- How many letters does the correct answer to this question contain?
- What is one more than the number of letters in the correct answer to this question?
- What is two more than the number of letters in the correct answer to this question?
- What is the lowest number
*n* for which you cannot answer the question: "What is *n* more than the number of letters in the correct answer to this question," if you have to give a simple answer (in words)?
- Or, see how far you can go and still come up with an expression to answer that same question for some
*n*.

Find as many answers as you can for each question (also see

here for some interesting ideas).

The phrase "added to fifteen" contains 14 letters, so appending this phrase to an answer for n will yield an answer for n+1. Its not straightforward, but it proves there is some written expression for all values n.

Q1. four

- 4 letters / value = 4

Q2. four added to fifteen

- 18 letters / value = 19

Q3. four added to fifteen added to fifteen

- 32 letters / value = 34

etc . . .