Minus' Solution to

Extra Efficient Elves
Posted Weeks of December 14 - 27, 1997

The idea is to put each elf to work as efficiently as possible. While keeping in mind that each type of wrapping paper is used for 1/4 of the presents.

To start:
Allie Elf gets the blue wrapping job. Later, since she is the fastest, she will do the red presents. Buzzy Elf gets the patterned wrapping job. Chelly Elf wraps the green presents.

There are 60,000 blue presents, so it takes Allie 20,000 minutes to do those. In that time, Buzzy wraps only 40,000 patterned presents and Chelly wraps 30,000 green presents.

Allie goes on to wrap the red presents. In 10,000 (more) minutes, Allie has wrapped 20,000 red presents (so she has 40,000 left). Meanwhile, Buzzy wraps 20,000 more patterned presents, so the patterned presents are finished. Chelly has also wrapped 15,000 more green presents, so she has done 45,000 in total.

Now Buzzy can help Chelly wrap green presents. In 6,000 more minutes, Allie has wrapped another 12,000 red presents (so 28,000 are left). Buzzy has wrapped 6,000 more green presents and Chelly has wrapped 9,000 more green presents. The green presents are finished.

Now there are only 28,000 red presents to wrap. In 6,000 more minutes, Allie has wrapped another 12,000 red presents, Buzzy has wrapped 6,000 red presents and Chelly has wrapped 9,000 red presents.

There are 1,000 red presents left. In 222 more minutes, Allie has wrapped 444 presents, Buzzy has wrapped 222 presents, and Chelly has wrapped 333 presents.

It takes Allie one half-minute for the remaining present. So, altogether, it takes 0.5 + 222 + 6000 + 6000 + 10,000 + 20,000 = 42,222.5 minutes, which is about 703.7 hours, or 704 to the nearest hour.