Solution: Bearly There
The best way to analyze this puzzle is to apply simple mathematics. If you count the parts of bears on each of the three strips, you will find 13 parts on the bottom strip, five parts on the shorter of the top strips, and eight parts on the longer top strip. When the strips are arranged with the longer top strip on the left, each of the bear parts on the bottom is matched up in a one-to-one-correspondence with the bear parts on the top strips. This one-to-one matching produces 13 complete bears with no missing parts. When the top strips are reversed and the shorter strip is placed on the left, there appear to be 14 bears. A careful examination will show that the bears in this position are not all complete. For example, one is missing a face—a trick that is cleverly hidden by the artist’s creative use of a bandanna. Also, in this position, there is not a one-to-one match between parts of bears on the bottom and top strips. The sixth bear from the left (which is wholly on the bottom strip) no longer has a separate matching part on the top strip and the seventh bear from the left (which is wholly on the top strip) no longer has a separate matching part on the bottom—again, a fact cleverly disguised by the artist. In this arrangement, there are 12 parts of bears on the bottom strip in one-to-one correspondence with 12 parts of bears on the top strips. The sixth part of a bear from the left—on both the bottom and top strips—has no match on the other strip. Thus, in this position there are 12 bears that have matching parts on the top and bottom strips, one bear that appears only on the bottom strip, and one that appears only on the top strip. Although these 14 bears look complete (other than the missing face), they are not as complete as the 13 bears in the other arrangement. Another way to show this is to measure the bears in both positions. The average height of the 13 bears is much greater than the average height of the 14 bears showing that the 14 bears are not as complete as the 13 bears.