152822

Solution A

Since there are 32 display boards and it must be a closed shape, I subtracted thirty two by one because it is the smallest whole number that is larger than zero and the question said that it must be as long and as narrow as possible. Then I did it again because there are two sides of the width of the rectangle. Now there 30 display boards left.

After that I divided it by two because there are two long parallel sides of rectangle, leaving the answer of 15.

In conclusion, 15 is the answer.