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Bn - Battalion (A battalion is a military unit of around 300–1,300 soldiers usually consisting of between two and seven companies and typically commanded by either a Lieutenant Colonel or a Colonel. Several battalions are grouped to form a regiment or a brigade.)
The terms 'problem' and 'gliding' refer to field training exercises. I believe the soldiers used these terms so their letters would not be censored. The name of a solider might have been modified slightly to avoid being censored.
August 4, the day my Uncle Paul wrote this, was also his birthday. This was his 21st birthday. What a way to celebrate, being in the middle of a war.
These type written letters to me are very interesting. They usually are not signed. One could think that someone else could type and send them. My father, even after the war, typed letters, and would end the letter with his typed name. Perhaps he picked up this habit while in the military.