If At First You Don't Succeed...

Programme Outline

Start to 03:35 - Setting the scene Lisa's path is blocked by three doors. She may pass if she can say what's written on the backs. After a little prompting, the Guard reveals that the number on the third door is seven more than that on the second, which in turn is five more than the number on the first.      The Wizard adds a further clue: the numbers add up to 39.
03:35 to 06:05 - The unknown Since Lisa is still stuck, the Wizard helps her out a little more. He starts by calling the number on the first door 'I don't know', which makes that on the second door 'I don't know plus five', and so on. Later, they replace 'I don't know' with 'x', so the doors are respectively x, x+5 and x+12.      Lisa starts trying to guess a value for x.
06:05 to 06:55 - The Mathematical Encyclopaedia The Encyclopaedia opens to page 'pi', and explores a method for producing progressively better estimates for the value of pi.
06:55 to 09:00 - Solving the problem Lisa's calculations (literally on the back of an envelope) suggest that x is 71/3. The guard, nervously, declines to admit defeat, but the doors open of their own accord. Lisa is, apparently, permitted to pass.
09:00 to 10:05 - Vexing the Guard The Guard, perturbed by what may have been a dereliction of duty, decides to calm his nerves with a spot of lunch. While his cabbage pie is tucked safely in his boot, his flask of tea is missing.      Lisa has pinched it, but offers to hand it back if the Guard can work out what x is if x2=20.
10:05 to 11:05 - Guessing The Wizard explains that guessing is one of the most powerful methods in mathematics. He draws a distinction between wild stabs in the dark and reasoned inspections of possible solutions.
11:05 to End - Square root The Guard is struggling with the arithmetic needed to solve his puzzle. Taking pity on him, Lisa produces a pocket calculator and uses the square root function to put him right. At last, the Guard is reunited with his tea.