The flag of the United States has 50 stars arranged in an alternating pattern: a row of six stars, then a row of five, etc. Alternatively, the star field can be viewed as a column of five stars, then a column of four, etc. This assemblage can also be seen as a four-by-five grid of stars interlaced within a five-by-six grid. See http://en.wikipedia.org/wiki/Image:Flag_of_the_United_States.svg for a good illustration. Since it is becoming allergy season for me, I happened to whip out my antihistamines and noticed that the 10 pills on a card are arranged in three rows: a row of three, a row of four, and a row of three. Or, in a one-by-four grid within a two-by-three grid. This got me wondering: what numbers can be represented as the total number of nodes (or stars or pills) where the nodes are laid out in two interlaced rectangular grids? For this problem, Im only considering the case where the numbers of rows for the two grids differ by exactly one, as do the numbers of columns (so a 1x4 in a 2x3 is ok, but not a 1x4 in a 3x6). This constraint makes it easy to alternate rows and columns to make adjacent nodes align diagonally instead of vertically. What I found more interesting than the numbers that can be represented is the set of numbers that cannot be represented: 1, 2, 3, 6, 9, 15, etc. (not in OEIS). 1 and 2 are trivial because there must be at least three rows. For every element after 2 (that Ive found) is a multiple of 3. The elements exhibit a decidedly non-regular pattern, and occur about half as frequently as primes. Can anyone point me to more information about this before I foolishly think that discovered something? Kerry Mitchell -- lkmitch@att.net www.fractalus.com/kerry