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Antek used his own key to solve the following extension: If each candle lasts three years, how many would be needed up to and including his 11th birthday? (see Candles Antek 1 attachment: attached to next submission form)

He explored and applied his method to the following extension task: If there are only 15 candles, how long does each one need to last to ensure that there are sufficient for every birthday, up to and including his eleventh? Through trial and improvement, he worked out that, if each lasted eight years, 17 candles would be needed: too many. So then he started again, giving each candle a 9-year life... and this only required 14 candles and hence, the answer was found! (see Candles Antek 2 attachment)