Seven Problems from Martin Gardner

  1. Can you divide an obtuse triangle into seven acute triangles?

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  2. a. Using a 7-minute hourglass and an 11-minute hourglass, how can you measure 15 minutes of time?

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    b. Using a 4-minute hourglass and a 7-minute hourglass, how can you\par measure 9 minutes of time?

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  3. Divide the yin-yang symbol (shown below) with a straight line\par that divides both the black region and the white region into regions\par with equal areas.

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  4. In a square oil field, a drilling rig is 21000 feet from one corner of the field, 18000 feet from the opposite corner of the field, and 6000 feet from a third corner. How far is the rig from the remaining corner?

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  5. In the diagram below, enter numbers into the squares so that the number appearing in the square labeled 0 gives the total number of 0's you entered in the diagram, the number appearing in the square labeled 1 gives the total number of 1's you entered in the diagram, etc.

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  6. In the diagram below enter the integers from 1 to 8 so that no consecutive integers are in circles that are connected with a line.

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  7. A hexahedron is a polyhedron with six faces. A cube is one example of a hexahedron and a pentagonal pyramid is another. How many essentially different hexahedra are there? (Two polyhedra are essentially different if one can be deformed into the other. For example a cube and a truncated square pyramid are essentially the same,but a pentagonal pyramid and a cube are not.)

    Solution