SOLUTION: There are 4 identical wooden blocks that are 20 inches long, 2 inches wide and 1 inch thick. If you glue them together, what is the difference of the largest and smallest outer sur

Obviously, to get the MAXIMUM surface area, you should glue the blocks together, attaching them at the minimal area faces.


So, you will get the MAXIMUM surface are, attaching the blocks at their 1x2 inches faces.


You will get then very long clued block with the length of 20*4 = 80 inches, the width of 2 inches and the thick of 1 inch.


Surface area of such a block is  2*(80*2 + 80*1 + 1*2) = 484 square inches.




To get the MINIMUM surface area, you should glue the blocks, attaching them together at their maximal area faces.


So, you will get the MINIMUM surface are, attaching the blocks at their 20x2 inches faces.


You will get then quite thick clued block with the length of 20 inches, the width of 2 inches and the thick of 4 inch.


Surface area of such a block is  2*(20*2 + 20*4 + 4*2) = 256 square inches.




Thus the difference of the largest and smallest outer surface area you can get is  484 - 256 = 228 square inches.