Making Ends Meet Puzzle - Solution
The Puzzle:
Hairy Mary At The Dairy they call her. That's not very nice, is it?
Anyway, Mary likes to eat her dinner by candlelight every evening. She saves all the candle ends because when she has collected seven ends, she can melt them down to make a new candle.
At the last count she found that she had 34 candles and 50 candle ends. One candle burns down in one evening. For how many evenings can Mary have a candlelit dinner before she has to buy more candles?
Clue: look at the title again!
Our Solution:Mary has enough candles for 47 evenings. Let's see why:
34 candles last for 34 evenings, making 34 more ends.
Add the 50 ends to make 84 ends, which is enough for exactly 12 new candles. (84 ÷ 7 = 12 remainder 0.)
These 12 candles last for 12 evenings, making 12 ends.
These 12 ends will make one new candle. (12 ÷ 7 = 1 remainder 5.)
This candle lasts for 1 evening, making 1 end. We now have 6 ends left, so we do not have enough for any more candles.
Total: 34 + 12 + 1 = 47 evenings altogether.
34 candles last for 34 evenings, making 34 more ends.
Add the 50 ends to make 84 ends, which is enough for exactly 12 new candles. (84 ÷ 7 = 12 remainder 0.)
These 12 candles last for 12 evenings, making 12 ends.
These 12 ends will make one new candle. (12 ÷ 7 = 1 remainder 5.)
This candle lasts for 1 evening, making 1 end. We now have 6 ends left, so we do not have enough for any more candles.
Total: 34 + 12 + 1 = 47 evenings altogether.
Puzzle Author: Stephen Froggatt