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**dkmathguy** A Japanese Samurai counted his soldiers remaining after a battle, by lining them in rows of different lengths, counting the number left over each time, and calculating the total from these remainders. A Samurai had 1200 soldiers at the start of a battle. After the battle, there were 3 left over when they lined up 5 at a time, 3 left over when they lined up 6 at a time, 1 left over when they lined up 7 at a time, and none left over when they lined up 11 at a time. How many soldiers were lost in the battle?