Brain Teaser

[El Salsero Gringo]

You have two pieces of string and a box of matches.
Your task is to measure a time interval of 15 minutes.
You know only that each string burns from one end to the other in exactly one hour.

How do you proceed?

(You can't be sure that the strings burn at the same rate all the way along, so measuring out won't help. Nor are the strings the same length as each other.)

[TheTramp]

Ummm. Simultaneously light both ends of one string, and one end of the 2nd string.

As soon as the piece of string that is on fire both ends is burnt out, 30 minutes have elapsed. Which means that the 2nd piece of string is now going to burn for another 30 minutes.

When you need your 15 minutes, light both ends of the 2nd piece of string simultaneously.

Next

[El Salsero Gringo]

Very good. But you could have PM'd me the answer and left it open a bit longer for other people!

Here's your second. No shouting out if you know the answer - and you - yes, you at the back - there's a detention if you don't behave. Now...

You are the new junior member of Acme Eggs' testing department, and responsible for implementing the European Union's proposed new standard for the strength of Egg shells.The test involves checking how many floors an egg from that day's laying may fall (into a Euro-standard garden flower bed) without breaking. You are to use Acme's 100-storey egg tower for the purposes of the test programme.

You are keen to make a good impression on your boss, naturally, and so wish to minimise the number of eggs that you break while testing - but also to complete the tests as quickly as you can so you can go and dance...

If you only had one egg, then of course you would start on the ground floor, drop the egg, if it didn't break then you'd go to the first floor, then the second and so on. Eventually you'd find the floor from which the egg broke - and that would be the test result. The maximum number of tests you'd need to complete would be 100 - if the eggs were too strong ever to break. On average, however, you'd need to do 50 tests (but see footnote)

The puzzle comes in two (maybe three) parts, getting harder:

Firstly (easy) suppose you had an unlimited supply of eggs - what is then the maximum number test drops would you *need* to perform to find the answer? What is the average number of tests you would have to perform? How would you go about the testing?

Secondly (harder) suppose you had exactly two eggs to use: what is the maximum number of test drops you'd *need* to do then? What about the average? How would you go about the testing?

Thirdly: generalise your result to n eggs.

You may assume that all the eggs laid on a given day are identically strong.

The winning entry will be distinguished by being accompanied by the best recipie for omlette. And my apologies to Lory - I have changed the wording to be less ambiguous in repsonse to your questions.

Footnote: To avoid pedantry in the use of the word 'average' you may assume the egg-strength is unknown, but equally likely to be any number between 1 and 100 inclusive.

[Dreadful Scathe]

set fire to both ends of the egg

then set fire to the factory and cry "oh but my test results were in there...sob :`( "

then buy in test results from a reputable independant body using the insurance money

these are too easy