A mathematical riddle : EXPERT LEVEL

in mathematics •  2 years ago 

Hi everyone, I'm new in the steem community and I have yet to make a proper article to introduce myself, but I'm eager to share with you one of my all-time favorite riddle. I like it because it is quite challenging, but it can be solved with a set of not so difficults steps with enough time and reflexion. Tell me in the comment if you like it or if you want some clue ! (I apologize in advance for english mistakes as it is not my mother tongue)

You are in a dark cell with your friend Bob, both captured by a mad mathematician who wants to test your thinking abilities.

" Tomorrow, you will be confronted with a test" he announces. "If you succeed, you will live. If you don't, you will die slowly"

"What is the test?" Bob asks.

"You're about to find out." he says. "Follow me"

The Mad Mathematician takes you to a smaller room with a single table at the center. On the table is a chess board with one coin on each square, either head or tail.

echecdamier.gif

"Tomorrow I will take you to this room again" The Mad Mathematician says, pointing his finger at you, "while Bob will remain in your cell. I will show you one square on the board. Your goal is to make Bob guess this square, and in order to do so you will be allowed to flip AT MOST one coin ! When I'll invite Bob into this room, he must be able to guess the square I chose only by looking at the chessboard, as you will not be allowed to exchange any word. Of course, you will have until tomorrow to discuss your strategy"

Bob looks at you fearfully. "How will we remember the positions of all the coins on the board by tomorrow?" He says.

"Oh I forgot to mention" interrupted the Mad Mathematician. "Tomorrow morning, before the start of your test, I will randomly flip the coins on the board. MWAHAHAHAHAHAHAH"

What strategy do you elaborate with Bob in order to survive? Good luck, and please don't give away the answer in the comments if you already know it!

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