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Black and White Hats
Black and White Hats
Four prisoners are given the opportunity of release and freedom if just one of them can work out the answer to a simple logic riddle. However, if they take part and one of them gives a wrong answer, or none of them can work out the answer at all, then their sentences will be doubled.
They are told that there are four hats. Two white and two black. Each man will have a hat placed on his head while blindfolded. When each man is wearing a hat the blindfolds will be removed. The prisoners will not be able to see their own hats and the only way they can work out what colour hat they are wearing will be from looking at the hats the other prisoners are wearing. All they have to do to win their freedom is for one of them to work out what colour hat he is wearing.
But there's a twist. To make it more interesting three prisoners stand in a line facing a brick wall. The prisoner at the back, A, stands on a box and can see both of the prisoners in front of him, B and C. Prisoner B stands on a smaller box and can only see prisoner C, who in turn can only see the wall. The fourth prisoner, D, stands on the other side of the wall and can see nothing of the other prisoners nor his own hat. They are not allowed to turn around, or converse in any way.
The prisoners are told that they have five minutes and to call out as soon as one of them thinks he knows for certain what colour hat he is wearing. But remember, if just one of them gets the answer wrong, they will all have their sentences doubled.
Within the time allowed one prisoner calls out the right answer. Can you guess which one, what colour hat he is wearing and how he knew for sure?
Four Knights Puzzle
Four Knights Puzzle
Here’s the setup. Four knights are placed on the corners of a 3×3 board. The goal is to get each knight into the opposite corner (that is, swap the knights on a1 and c3 as well as a3 and c1).
Can it be done using legal chess moves, and if so, what’s the minimum number of moves?
(A knight can move to an unoccupied space according to an L-shape movement: it must move two spaces horizontally and one vertically, or two spaces vertically and one horizontally.)
Poisoned Chocolate Game
Poisoned Chocolate Game
A bar of chocolate has 3 x 6 squares, with the corner one poisoned. Two players alternately break off a piece in a straight line along the grooves and eat it! The Player who leaves the poisoned square for his opponent is the winner.
What is the strategy for winning and what is the general strategy for a bar of m x n squares.
Further Reading
Further Reading
The following book will realy improve your ability to answer this sort of puzzle. Consider booking in 3-4 sessions with me to work through specific puzzles on the tutoring page below.
Algorithmic Puzzles Anany Levitin & Maria Levitin
Amazon: Algorithmic Puzzles: Amazon.co.uk: Levitin, Anany, Levitin, Maria: 8601406057036: Books
While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer ex&les from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures.
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