Puzzle 1: Mutilated Chessboard A chessboard has 64 squares alternating black and white, and you also have 32 dominoes th

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Puzzle 1 Mutilated Chessboard A Chessboard Has 64 Squares Alternating Black And White And You Also Have 32 Dominoes Th 1 (220.1 KiB) Viewed 51 times

Puzzle 1: Mutilated Chessboard A chessboard has 64 squares alternating black and white, and you also have 32 dominoes that are the same size as two squares of the chessboard. There are many ways to place 32 dominoes so ::. that every square of the chessboard is covered. But is it possible to cover this mutilated chessboard of 62 squares (where two opposite corners are removed) with 31 dominoes? (A) Identify and discuss some important aspect of this puzzle's wording, eg something that is unclear/ambiguous, or some information that is missing. State the assumptions you are making to manage the ambiguity or lack of information. (1+1 = 2 marks) (B) Describe an invariant (recall the orange juice and water puzzle) that simplifies the puzzle and lets you simply prove whether it is possible or not. (1 mark) Puzzle 2: 3 light bulbs, 3 switches... There are 3 switches outside a room which control 3 light bulbs inside it. You may flip the switches as you like, but you can only enter the room once you have finished flipping the switches. You can't see the light bulbs from outside the room, and you're only allowed in the room once! Is it possible to determine which switch controls each bulb? (C) Most people make an assumption about the solution that makes this puzzle impossible. What is the assumption, and discuss two reasons why this assumption is usually made. (2 marks) Puzzle 3: If in doubt... Reuben is twenty-six, lives with his parents, and has a beard. A first class honours graduate majoring in computer science, he built and flew drones while at university. Which statement is more probable: “Reuben works as a life coach” or “Reuben works as a life coach and loves playing computer games”? (D) State you answer and explain why it is correct. (1 mark) Ac Ga