Page 285 - HOW TO PROVE IT: A Structured Approach, Second Edition

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More Examples 271

Figure 1

Figure 2

n
n
Example 6.2.4. Prove that for any positive integer n,a2 × 2 square grid
with any one square removed can be covered with L-shaped tiles that look like:
this:

Scratch work
n
Figure 3 shows an example for the case n = 2. In this case 2 = 4, so we have
a4 × 4 grid, and the square that has been removed is shaded. The heavy lines
show how the remaining squares can be covered with five L-shaped tiles.