Answer to Riddle #69: Combing the Dregs of Glasses to Make a New One

69. At a whisky tasting Mr Cheap works out that for every 10 used, empty, glasses he can collect, he can poor the dregs together to make a whole new glass of whisky. At the end of the day he is able to find 100 empty glasses. How many full glasses can he now drink?

When I found this puzzle it was about collecting cigarette butts (below). I changed it because I thought this was nicer:

Full glass of whisky to illustrate this puzzle.Before reading the answer can I interest you in a clue?

Just a quickie here with a simple trap to avoid. Obviously the easy and wrong answer is 10. That is 100 empties divided the 10 we need makes 10 full glasses...

We can then take the ten glasses we have made and combine them in to one new glass. The answer is 11.

There are some other interesting numbers:
100 → 11
108 → 11
109 → 12
1000 → 111

Alternate Versions

When I stumbled on to this puzzle it looked like this:
As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?
I thought that was a bit unpleasant. Then I found this one:
A confectionery shop owner allows children to purchase a chocolate in exchange of five wrappers of the same chocolate. Children from the locality consumed 77 chocolates in a month. Now, they all collected them together and decide to buy back chocolates. How many chocolates do you think they can buy using those 77 wrappers ?
They're all basically the same, the same trap.

Both AI's got this wrong, not realising that there was a second round to the puzzle. But performing a simple arithmetic operation.

If you're curious what Bard made of this puzzle...

If you're curious what ChatGPT made of this puzzle...

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