The Ants Go Marching Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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This is a puzzle cache. It is not at the listed location. Find the true location from the information below.
Unlike some of my previous puzzles, there is no hidden information. Just solve the problem to get the final coordinates.
This is an original puzzle I invented while in grade school in the early 60s. I was finally able to solve it using only the analysis skills of my seventh grade pre-algebra class, so it should not be too hard.
The First To Find this cache was JayB10 and kelinore
The following have sent in the correct bonus answer: Fat Chuck, teamajk, fmoraes, theLadyBee, VPPLAYER, baronvonben, ---.
I just found out that this cache was featured as the Geocaching Puzzle of the Day at this blog. Thanks.
Problem - The Ants Go Marching
A popular song at camp and while riding the bus to camp was "The Ants Go Marching..."
The ants go marching one by one.
Hoorah! Hoorah!
The ants go marching one by one.
Hoorah! Hoorah!
The ants go marching one by one;
The little one stops to suck his thumb,
And they all go marching round and round and into the ground
And out in the rain and back again.
Boom, boom, boom, boom!
The ants go marching two by two.
Hoorah! Hoorah!
The ants go marching two by two.
Hoorah! Hoorah!
The ants go marching two by two;
The little one stops to tie his shoe,
And they all go marching round and round and into the ground
And out in the rain and back again.
Boom, boom, boom, boom!
The ants go marching three by three.
Hoorah! Hoorah!
... you get the idea - it continues counting up to...
The ants go marching ten by ten;
The little one stops to shout
"THE END!!"
What is the smallest number of ants that could have started the song?
Assume the ants are marching single file in the first verse, two across in the second verse, three across in the third, etc. up to ten across. Also assume that during each verse the ants are marching in complete rank and file. That is, there are no partial rows or columns. And finally, as indicated, at the end of each verse a single ant leaves the group.
Your answer will be in the form ABCDEF (six digits – any of which could be zero).
Bonus question: For bonus points, send me a simple closed-form mathematical expression that describes all solutions, not just the smallest.
40° [A-A][D-B].[C-A][F-B][C+B]
83° [F-F][B-A].[D+E][C+E][D-E]
This cache is now at its third location. The above formula and the geochecker have been updated. There is parking east of the new GZ. Also there is a different container.
These ants always seem to be marching to a new location! Perhaps in addition to asking HOW MANY ants were marching I should have been asking WHY they were marching. The answer is obvious. Like all ants they must have been looking for a picnic to raid! In the first location, a growling dog chased them off. In the second location they were bivouacked in a bush that got whacked. Finally at the third I may have found a location to make them happy. There is a nice (and popular) picnic area nearby. May they finally stop marching! 
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Additional Hints
(Decrypt)
Chmmyr: Cvpgher gur oybpxf bs nagf znepuvat va rnpu irefr.