Beginning Pentomino Problems Nearly all of the problems in this section require less than the full set of twelve pentominos, which make them a little easier. A-1 The example below shows how three pentominos can be 3 x 5 Rectangles. put together to make a 3x5 rectangle. Find another rectangle of the same size using the and pentominos. See N, P, U how many of the other five ways of building this rectangle you can find using different combinations of pentominos. A-2 This rectangle is formed using four pentominos. 4 x 5 Rectangles. Find at least two other ways of filling a rectangle of the same size using (a) four pentominos. (b) Find a solution where a pentomino piece does not touch the outer edge of the rectangle. (c) Find a solution so that the four pentominos used touch at the same point. (This is called a solution.) crossroads (d) Find a solution so that the rectangle can be divided into two identical shapes. A-3 Now we have a square that is built from five pentominos. 5 x 5 Squares. (a) Find at least two other ways of filling a square of the same size using five pentominos. (b) For each pentomino, try to find a solution where the given piece does not touch an edge. Does this answer change if the pentomino were not used in the I solution? A-4 Including the three problems, there are 14 Many Rectangles. rectangles that can be constructed that do not use the full set of pentominos. One of the rectangles is very simple to solve, even easier than the first problem.
Beginning Pentomino Problems Nearly all of the problems in this section require less than the full set of twelve pentominos, which make them a little easier. A-1 3 x 5 Rectangles. The example below shows how three pentominos can be put together to make a 3x5 rectangle. Find another rectangle of the same size using the N, P, and U pentominos. See how many of the other five ways of building this rectangle you can find using different combinations of pentominos. A-2 4 x 5 Rectangles. This rectangle is formed using four pentominos. (a) Find at least two other ways of filling a rectangle of the same size using four pentominos. (b) Find a solution where a pentomino piece does not touch the outer edge of the rectangle. (c) Find a solution so that the four pentominos used touch at the same point. (This is called a crossroads solution.) (d) Find a solution so that the rectangle can be divided into two identical shapes. A-3 5 x 5 Squares. Now we have a square that is built from five pentominos. (a) Find at least two other ways of filling a square of the same size using five pentominos. (b) For each pentomino, try to find a solution where the given piece does not touch an edge. Does this answer change if the I pentomino were not used in the solution? A-4 Many Rectangles. Including the three problems, there are 14 rectangles that can be constructed that do not use the full set of pentominos. One of the rectangles is very simple to solve, even easier than the first problem.
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