7. Logical Puzzles

I was chatting to my daughter, Ruth, on the phone yesterday and she mentioned that she was struggling to solve the latest of a series of regular puzzles posted by Alex Bellos in the Guardian newspaper.  The puzzle, which is called The Three Switches, is as follows:

The Three Switches

Downstairs in a house are three identical on-off switches. One of them controls the lamp in the attic. The puzzle is to work out which switch controls the lamp.

The rules are as follows. You are allowed to manipulate the switches all you like, and then you are allowed only one trip to the attic. How do you do it?

You might like to have a go at the problem yourself before reading on.

Ruth pointed out that the problem seemed to be impossible. If there had been just two switches the question would be trivial but with three, there wasn’t enough information to solve it. From my personal experience of tackling these sorts of puzzles, I work with the following assumptions.

1. Since the problem has been posed, it must be solvable (unless there has been a misprint, which is unlikely).

2. If I have reached the point of finding it impossible, then there must be an extra dimension or layer of information available to me that I have not yet considered.

In this particular case, the restriction in most people’s thinking (mine included, I have to admit) is that they only consider their sense of vision to test the lightbulb. But (most) lightbulbs also generate heat and this is the missing link for tackling this puzzle. If you were unable to solve it before, have another go with this hint in mind. And when you’re ready, check your solution against my 2-minute video below.

Solution

Interestingly, Bellos claims that he offered this puzzle to many people from a wide variety of backgrounds and only one was able to solve it directly. This was Jo Nesbø, a well-known Swedish crime writer. Perhaps this is not surprising, since crime writers make an art form out of misdirection, to ensure that the reader only finds out the answer right at the end. So perhaps Nesbø's mind was well prepared for the sort of lateral thinking that this puzzle might required.

If you like these sorts of puzzles, Bellos has put together a nice collection at:

http://snewsi.com/lite/a/Alex+Bellos/all

More lightbulbs

And talking of lightbulbs …

Hannah’s Sweets
Over the past couple of weeks I’ve had a number of emails from friends drawing my attention to the recent hullabaloo about a GCSE exam question – referred to as ‘Hannah’s sweets’. The outcry from students has been that this question was too hard. Anyway, here it is. Have a look and see if you can answer it. 

If you'd like to see a solution, I’ve posted one here.  

Postscript

This post looked at the puzzle, The Three Switches. I also looked briefly at a GCSE question from this summer's mathematics exams that has upset a few people. 
If you are interested trying some more puzzles, have a look here in my website, www.MathinPictures.co.uk.