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#1 2021-09-25 08:45:21


Maths Problem solving

Winston is playing a simple game of Battleships, involving a single 'battleship' of 4 squares in a
line placed on a 10 by 10 square 'sea'.
The Opponent selects a position at random for the battleship, but does not show Winston where it
is. Winston takes a shot, i.e. names a square and is told whether it is a hit or a miss. He continues
to try squares until all four parts of the battleship have been hit and it is then considered to be
sunk. The aim is to sink it with as few shots as possible.
Winston always chooses a 'good' square, i.e. one that is not less likely than any other to be a hit,
based on what he knows at the time.
(a) (i) How many possible positions for placing the battleship are there?
(ii) How many 'good' squares are there at the start?
Winston is very lucky and gets a hit on his first shot.
(b) (i) How many possible positions could the battleship be in?
(i) How many 'good' squares are there now, and where are they in relation to the hit?

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