Egg Timers: Use 7 and 11 to Make 15

Date: 09/20/2001 at 21:56:01
From: Kathy
Subject: Brain twister problem

If you have only 7-minute and 11-minute hourglass egg timers, how can 
you time the cooking of an egg for 15 minutes?

I've tried different ways to combine 7 minutes and 11 minutes and I 
always get it wrong.

Date: 09/21/2001 at 12:51:28
From: Doctor Wolfson
Subject: Re: Brain twister problem

Hi Kathy,

The way I'd start this problem is to figure out a few ways of using at 
least one of the given numbers to get to 15, and then decide what's 
left. 

For instance, you have a seven-minute timer, so if you could get one 
minute of sand by itself (in either timer) then you could put the egg 
in when the minute starts, and when the minute runs out, let the 
7-minute timer run for two full turns (14 more minutes) before taking 
the egg out.Similarly, if you could get 4 minutes by itself, then you 
could put the egg in when the 4 minutes start, then start the 
11-minute timer when the 4 minutes run out.

So now we have to figure out how to get either 1 minute or 4 minutes 
measured out. It would take a lot of combinations of 7's and 11's to 
find a difference of 1, so that probably isn't the fastest way to get 
there. But 11-7 is 4, so we have some hope.

What if you started both timers at the same time (without putting the 
egg in yet) and let the 7-minute timer run out? How much would be left 
in the 11-minute timer? Does this give you a hint as to when to put 
the egg in, and what to do next? It's similar to the first suggestion 
I gave, in looking for the 1+7+7 minute answer.

So the idea to remember is to work backward from the answer you need, 
and decide what will happen just before that. I hope this will remind 
you of a way to combine the numbers that you can work with.

I hope this helps. Feel free to write back if you'd like more 
clarification.

- Doctor Wolfson, The Math Forum
  http://mathforum.org/dr.math/