During my last visit to the UK. I spent a few days in a small town, where I stayed as a paying guest with a British landlady. The heaters in the rooming house were all coin operated. One day my landlady requested my help in sorting out a problem. There were one hundred and twenty coins in her gas meter and one of them, she knew, was counterfeit. The counterfeit coin was either heavier or lighter than the others. Now the problem was to isolate this counterfeit coin and find out whether it was lighter or heavier, in five weightings. How can one do it?