Basically what the Army did was cut off the poles and lay the world flat. They took the world and created 6 x 8 degree squares. These have a number/letter designation. Since this was too large they cut it down further into 100,000 meter squares and gave these a letter/letter designation. Then this grid will end up as 10,000 meter squares, at this point you are using number/number designators, due to the fact that this square is broken down into 1000 meter squares. So if you are on the ground and you want to give your position in UTM you use even numbered coordinates, for example: 567 123 There are six numbers here. Six numbers gets you down to within 100 meters of your position. 5678 1234 gets you to within 10 meters. The more nubmers you have the more accurate you are. This system was originally developed for artillery so shells could be called in on an exact position. The way you read the map is from Left>to right>then up^. So you start at the bottom read left to right then go up along the side.
So at Calispell peak in Easter Washington the coordinates would be 11U(grid zone designation) MD(100,00 m sq. desig.) 6298 6489= 11UMD629648. These would be your exact coordinates at the top of the peak.
I hope I haven't confused you too much and have explained it ok. If you have any more questions just let me know. Take care.
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Yol bolsun,
Jamie