The Universal
Language
Red Nose Puzzle
This puzzle is about a red nose toy. The toy contains a 4x5 board and a control handle that can slide along the grids. In every square, there is a boy's face, which has either a red nose or a white nose. When you play, you can slide the control handle gently along the grids up or down, right or left. Once a square is passed by the handle, the nose of the boy in that square will change colour, either from red to white or from white to red.
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Question
- If the initial pattern of the board and the initial position of the control handle is given as shown in the picture on the left, how should we move the control handle so as to obtain the pattern of the board in the picture on the right? Make sure the control handle stops at the top left corner (a,1). Try to find the shortest path.
- Given any initial pattern of the board and position of the control handle, is it always possible to reach the state shown in the picture on the right? If yes, give a general algorithm; if no, give a counter example.
Answer
My friend Shi Cong and I collaborated closedly on this project when we took the module "network optimization" together. We did purchase a real red-nose toy to play with. Undoubtedly, playing the actual toy was much more enjoyable than drawing the them on paper. (~_^) Here is our report.
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