Unit Fractions - Pyramid Power?

Update as of 6-2-07: All solutions to the problem below are now posted in the Comments section. Also, read Eric Jablow's astute comments and his challenge to students!

The following problem is well-known, however it is an excellent exercise for middle schoolers and as a challenge for older students as well.
Target Audience: Grades: 6-12
Prerequisite skills: Basic understanding of fractions and simple operations
Develops: Logical thinking, Systematic Counting/Listing, Fraction Concepts, Structure of Mathematical Proof
Recommended Classroom Organization for this activity: Students working in groups up to 4.
Online Resource: Here's one of the best sites on Egyptian Fractions I have found on the web. The problem is discussed but not solved!

Introduction for student:
A unit fraction is defined as 1/n, where n is a positive integer greater than 1.
The number 1 can be written as a sum of 3 unit fractions in 3 ways:
1 = 1/2 + 1/3 + 1/6
1 = 1/2 + 1/4 + 1/4
1 = 1/3 + 1/3 + 1/3
No other ways (other than rearrangement) can be found using the following reasoning:
The largest of the 3 fractions could not be less than 1/3. Why?
If 1/3 is the largest fraction, then the larger of the remaining fractions could not be less than 1/3. Why?

Here's your challenge:

There are 14 ways to write 1 as a sum of four unit fractions of the form:
1 = 1/a + 1/b + 1/c + 1/d, where a ≤ b ≤ c ≤ d.
Make a list of all of these ways. Have fun! Uh, no calculators please!