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November 2020 - Math Problem

There are seven seats on a boat all in one line from front to back.

Only one person can be on a seat at any point in time.

The seat at the centre of the boat is empty and the other six seats are occupied.

The three people at the front of the boat want to move to the back of the boat and the three people at the back want to move to the front of the boat.

A person may move to the next seat if it is empty or may step over one person to get into an empty seat.

What is the minimum number of moves required to reach their goal?

Solution:

It will take 15 moves.

What if there were 11 seats on the boat and 5 people in the front and 5 in the back?

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