vegetarian lasagne, black coffee

[pigseatingfigs]

OK all you intelligent people, how can I formally represent uncertainty in distances? That is, I want to be able to say, X is a certain distance and angle from Y, but both of these are within +-20%, or something similar. I also need a way of comparing statements so that one with less uncertainty can be given priority. Try to make it in the form

Comments

[chickenfeet2003]

I think the string problem requires that the strings be identical and burn faster or slower in some relatively uniform way.

Cut the strings into eight equal lengths maintaining the order and orientation of the strings. Light the same end of each eight string. If the eighths burn for the same time, your 15 minutes will be measured by burning, sequentially, the second 1/8 of one string and the seventh 1/8 of the other. If the eighths take different amounts of time then burn the second 1/8 of each string consecutively.

[pigseatingfigs]

Not quite.... you're on the right track though. The strings are not identical, unfortunately. If you light each end of one of the pieces of string, the whole thing will take exactly half an hour to burn (why?). Can you see the solution now?

[chickenfeet2003]

Light both ends of one string and one end of the second string. When the first string is burnt immediately light the unlit end of the second string. In a further 15 minutes the second string will be completely consumed.

[pigseatingfigs]

yay! well done.
Now.... can you think of a way of measuring 15 mins with just one string? You will never be able to get *exactly* 15 mins, but you can get very close...

[chickenfeet2003]

Divide he string into four equal pieces. Light one end of each piece. Wait until two pieces have burnt out then light the free ends of the remaining two strings. Your approximation to 15 minutes is up when the third string is burnt out.

[pigseatingfigs]

That's good! but a more accurate way (in that it can allow for greater variation in burning speeds across the string) would be like this:
Light each end of the string, and what is approximately the centre. If one of the pieces of string burns up completely, light the centre of the remaining piece. Keep doing this. You have to keep the string burning in 4 places at all times. To get 15 mins you would have to light the centres an infinite number of times (and the piece would become infinitey small, also you would have to move incredibly quickly). But you would be able to get 15 mins within a few seconds quite easily.