### Problem 258: Pandora’s present

Petula Penniful is a wealthy and flamboyant woman who spoils her son Freddy (and herself) rotten. Her relentless doting culminates annually on Freddy’s birthday. When her son turned six, she bought him a pony. The following year, an entire petting zoo. With Freddy’s eighth birthday approaching, she sashays into Top Toys Unlimited and booms, “I’ll take one of everything.” Store clerks busily stuff action figures, toy trucks, puzzles, and games into gift boxes. They stack the cubeshaped boxes from largest to smallest at the gift-wrap counter. Top Toys carries so many playthings that the number of boxes is infinite.

The edges shrink in feet from one box to the next according to the series:

And so on to infinity.

Help the gift-wrap attendant by answering two questions: What is the exposed surface area of the tower of boxes? What is the volume of the tower?

### Winners circle

Fun problem 256: Smart ass, April, 2002
Total entries: 32
Number correct: 23 (72%)
Winner: Denis Rehse, Largo, Fla.
Denis’s prize: The Fluke 179 multimeter is designed for demanding industrial environments with a CAT IV rating, 6,000 count resolution, 0.09% accuracy, and the ability to measure min/max/average, true-rms, ac voltage, current, and temperature.

Get your creative juices flowing and send us your original problems and solutions. If we publish yours, you’ll win a prize.