Numeracy Task 2 – Flipping Hidden Cups

A round table has four deep pockets equally spaced around its perimeter. There is a cup in each pocket oriented either up or down, but you cannot see which. The goal of the game is to get all the cups ‘up’ or all the cups ‘down’. You do this by reaching into any two pockets, feeling the orientation of the glasses, and then doing something with them, (you can flip one, two, or none). However, as soon as you take your hands out of the pockets the table spins in such a way that you can’t keep track of where the pockets you have visited are. If the four glasses ever get oriented all up or all down a bell rings to signal you are done. Can you guarantee that you will get the bell to ring in a (maximum) finite number of moves, and if so, how many?

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You can find out more about Numeracy Tasks in my ‘Pair-a-Dimes’ blog.
I will tag all tasks like this with Numeracy so that they are easy to find in one location.

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