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| April Extra Credit | |||||||||||
| Pentominoes are shapes that can be created by joining five congruent squares edge to edge. There are twelve possible shapes. Try to figure out all 12 shapes, or ask Dr. Cohn if you would like a copy of the 12 shapes. Solomon Golomb, a mathematician, created a game where two players alternately place pieces from a complete set of 12 pentominoes on the squares of a checkerboard. The first player who cannot place a piece without overlapping another piece is the loser. The first four extra credit problems of the month feature pentominoes. | |||||||||||
| Week of April 2nd: | |||||||||||
| Since there are only 12 different playing pieces, no pentominoes game can last more than 12 moves. The shortest possible game on an 8 x 8 board ends in 5 moves. Find five pieces, that when placed on an 8 x 8 grid would make it impossible for another move to be made. | |||||||||||
| Week of April 9th: | |||||||||||
| Place three different pentominoes on a 6 x 6 grid so that no more pieces can be placed on the board. Find a second solution using completely different pentominoes. | |||||||||||
| Week of April 16th: | |||||||||||
| Place four different pentominoes on a 7 x 7 grid so that no more pentominoes can be placed. Find a solution in which one of the pentominoes touches the edge of the grid. | |||||||||||
| Week of April 23rd: | |||||||||||
| Place six different pentominoes on a 9 x 9 grid so that no more pieces can be placed. What about seven pentominoes on a 10 x 10 grid? These two problems will require you to use a different approach than the previous problems. | |||||||||||
| Week of April 30th: | |||||||||||
| King cobra eggs have a 70 day incubation period. Seven king cobras lay their eggs 7 days apart, then 5 days after these eggs hatch, 8 more king cobras lay their eggs 6 days apart. How long will it be until all of the eggs have hatched? | |||||||||||