Alice and Bob are candle makers, but they have ran out of material. They decide to go dumpster diving for burnt out candles. They realize that if they melt three old candles they can make a new one. Alice manages to find 10 old candles and Bob also finds a handful. How many candles can Alice make for her own use?
First Alice uses 9 out of her 10 candles to create 3 new ones. She then has 3 candles + 1 burnt out. After using her 3 new candles she can once again use them to create a new one, leaving her with 1 candle + 1 burnt out (total of 4 new candles made). After using the new candle she is left with 2 burnt out candles. She Now borrows one of the candles bob found and uses it together with the two she has to create a final candle (in total 5 now). After using the candle she hands back the burnt out one to Bob. She has now made and used 5 candles form the 10 she started with, giving back all that she borrowed from Bob.