Coin touches coins

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?




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A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

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Only one color, but not one size,
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Artificial Intelligence

Artificial Intelligence has crushed all human records in the puzzle game “2048,” achieving a high score of 839,732 and beating the game in only 973 moves without using any undo.