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Cookie Conundrum (Biscuit Baffler in the UK version) is a puzzle in Professor Layton and the Unwound Future.

Puzzle

US Version

There are 15 cookies to share amongst a large group. The first person eats one cookie then passes two equal portions of the leftover cookies to two other people. They both eat a cookie then each pass two equal portions of their remaining cookies to two other people, and so on until all of the cookies are gone.

It takes one minute to eat a cookie. Ignoring the time that it takes to pass them, what's the shortest amount of time it could take for all of the cookies to be eaten?

UK Version

You have 15 biscuits to share among a large group. The first person eats one biscuit and then passes two equal shares of the remaining biscuits to two other people. They both eat a biscuit, and both pass two equal shares of their remaining biscuits to two other people, and so on until all the biscuits are gone.

It takes one minute to eat a biscuit. Ignoring the time it takes to pass them, what's the shortest amount of time, in minutes, that it would take for all the biscuits to be eaten?

Hints




Click a Tab to reveal the Hint.

US Version

Visualizing exactly what the puzzle is describing as a scene in your mind might be all you need to figure this one out.

UK Version

Drawing a diagram is the quickest way of working this one out.

US Version

Try and break the problem down into numbers. If one out of 15 cookies is eaten, that means 14 are left. If you divide those 14 in half and pass them to two people, they each get seven. That's taken one minute so far.

If you think about that problem in concrete mathematical terms like this, you should be able to figure it out.

UK Version

Try and break the problem down into numbers. If one of the 15 biscuits is eaten, that means 14 are left. Divide those 14 equally between two people, and they get seven each. That's taken one minute so far.

Think about the problem in concrete mathematical terms like this and you should be able to work it out.

US Version

The two people who get seven cookies each eat one cookie, which takes one minute. They both have six cookies left and divide those in half, then pass three cookies to two people each. That's two minutes so far.

UK Version

The two people who get seven biscuits eat one biscuit each, which takes one minute. They both have six biscuits left, which they each divide between two people, giving those people three biscuits each. That's two minutes so far.

US Version

The people who receive three cookies each eat one of them, so they each have two remaining. That's three minutes elapsed at this point.

If you divide these two cookies in half and pass one cookie to each of the next people in line, how many more minutes will it take to finish the cookies?

UK Version

All the people who receive three biscuits eat one of them, so they each have two remaining. Three minutes have elapsed at this point.

If you divide these two biscuits between the next people in line, giving them one each, how many more minutes will it take for the biscuits to be gone?


Solution

Incorrect

Too bad!

US Version

Clear your mind, and think about it again.

UK Version

Clear your mind and think about it again.

Correct

US Version

Correct!

The cookies will be gone in four minutes.

The diagram above shows how you can visualize the puzzle to help you solve it. This seems like the kind of thing that might be useful in real life, but it's not a situation that arises very often, is it?

UK Version

Crumbs!

The biscuits will be gone in four minutes.

The diagram above shows how you can visualise the puzzle to help you solve it. This seems like the kind of thing that might be useful in real life, but it's not a situation that arises very often, is it?

UF030S

A big thanks to http://professorlayton3walkthrough.blogspot.com