MathDB

In assigning dormitory rooms, a college gives preference to pairs of students in this order:

AA,\, AB ,\, AC, \, BB , \, BC ,\, AD , \, CC, \, BD, \, CD, \, DD

in which

AA

means two seniors,

AB

means a senior and a junior, etc. Determine numerical values to assign to

A,B,C

and

D

so that the set of numbers

A+A, A+B, A+C, B+B, \ldots

corresponding to the order above will be in descending order. Find the general solution and the solution in least positive integers.

A4