You are to find 10 caches whose coordinates are of the form N/S xx° AB.CDE E/W yyy° FG.HIJK such that A,B,C,D,E,F,G,H,I,J are all distinct, which we will unabashedly refer to as a dgaussian point or "dg point" for short. Note that this cache itself is a dg point.
Consider a typical N/S xx° E/W yyy° sector of the globe, and the points AB.CDE, FG.HIJ within it. (There are 180×360 such sectors.) Let's do some counting: A and F can each be any of the six digits selected from {0,1,2,3,4,5} whereas B,C,D,E,G,H,I and J can be any digit at all. Thus there are 36×108 points in the sector. But in how many of these are all the ten digits distinct? For A there are six possibilities. Once it's selected that leaves five possibilities for F. Then that would leave 8 possibilities for B, 7 for C, ..., 2 for I and J gets stuck with whichever digit is left. All totaled there are 6×5×8×7×6×5×4×3×2×1 = 1,209,600 such points in the sector. So the fraction of points in the sector that are dg points is 1,209,600/3,600,000,000 = 336/1,000,000. That is, for every million points only 336 are dg points.
Today there are about two million geocaches in the whole wide world. If caches were placed at random, then about 672 should be dgpoints. You're to find only ten of them.
What counts? Any cache whose given coordinates are of the form N/S xx° AB.CDE E/W yyy° FG.HIJ such that A,B,C,D,E,F,G,H,I,J are all distinct. Puzzle solutions can be included too only it it is explicitly stated on the cache page that the solution has that form.
Please note that Oops! does not qualify although it is prt of the star series many of which do.