The Clever Old Woman

OK, here's a challenge for my blog readers. It's a brain teaser. See if you come up with the correct answer. Here goes.

Long ago in the days when people used candles to light their houses, there lived an old woman. She was poor but very clever. She thought of many ways to save money. One way she saved money was by making new candles from old ones. She found that one quarter of a candle never burned because it was inside the candle holder. Most people just threw away these unburned candle stubs but the old woman saved hers. By melting four of these stubs she could make one new candle.

One day the old woman went to the candle maker's shop and bought sixteen candles. How many new candles could she make from the left over stubs of the sixteen candles?

NOW STOP READING AND WORK IT OUT.

I confess that nobody in our family (including Dad) got the correct answer. We all took it on face value as a simple maths question and said the answer was four candles. Did anybody work out the correct answer, which is five candles?

The clever old woman made five new candles. Every four candles gave her four quarters from which to make one new candle. So from the sixteen candles she made four new ones. I guess we all got that far. But those four candles also gave her four quarters from which she could make a fifth candle.

We found a great book full of this sort of puzzle from a second hand shop. If anybody likes this sort of thing, I'll post more from time to time.