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Puzzle 1: 2007 triangles.Draw some segments in the plane to form exactly 2007 triangles. | |
Example 1: 10 segments form 35 triangles. |
Example 2: 2009 segments form 2007 triangles. |
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Your goal is to use minimum number of segments.
Score: 50 points for the best solution, 45 - for one segment more, and so on. Your solution is wrong if you draw more or less then 2007 triangles. | |
Puzzle 2: 2007 paths.Consider all different paths from top left corner to bottom right corner of rectangle with a grid. Path can go only from left to right or from right to bottom along the grid lines. Some grid nodes are marked - path cannot go through this nodes. | |
 | There are four paths from top left corner to bottom right. If grid node is not marked then there are ten paths. |
| Make sure there exist 48620 paths in the 9x9 square. Your goal is to mark some nodes to make number of paths equals to 2007. |
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| Score: 40 points for any solution, 50 points if your solution has minimum number of marked nodes. | |
Puzzle 3: Penta-parquet.Pentatriangles are the set of twenty pentagons divided into five triangles. Some of the triangles are black, some are white. All possible combinations of black and white colors are used. Place the set into the given grid. Every triangle can be reflected from top to bottom or from left to right. This puzzle has two parts solved separately: A. Make maximum number of isolated black domains. B. Make maximum area of one of the black domains. Area is the number of triangles. | |
 | There are 17 black domains in the example. Maximum area is 9. Sum of two parts is 26. |
| Score: 50 points for maximum sum of parts, 45 - for the next and so on. | |
Puzzle 4: Square cutting.You have square 5x5 with a grid: Draw some number of segments with ends in the grid nodes on the square edges. Try to obtain maximum number of parts with different areas. | |
| Example: three segments cut the square 4x4 into the six parts. All parts have different area: |
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| Score: 50 points for the best solution, 45 - for the next and so on. | |
Puzzle 5: Penta-ring.Penta-ring is position of 12 pentaminoes on the grid. Every pentamino have common bounds with exactly two other pentaminoes and cannot touch other elements even a corner: Elements can be rotated and/or reflected. Make penta-ring having maximum sum of bounds. In the example this sum (all bounds are marked by bold line) is equal to 29. Score: 50 points for the best solution, 45 - for the next and so on. | |