Find four whole numbers such that every whole number up to 12 is the sum of at most two of them, that is, either the number is one of them, or it is the sum of two different ones, or it is the sum of two equal ones (it is a “double”).

Here are the numbers from one through twelve:

1       2       3       4       5       6       7       8       9       10       11       12

Which four do you choose?______      _______      ________      _________

Show that the four you choose actually work, that is, show that each whole number from one through twelve is the sum of at most two of them. List your solutions below.

(If it is not clear to you what this problem is asking you to do, just email pbaggett@nmsu.edu.)