# A General And His Soldiers

In ancient China, generals counted soldiers remaining after a battle by lining them up in rows of diﬀerent lengths.

If a general had $$1200$$ soldiers at the start of a battle and if there were

$$1)$$ $$3$$ left over when they lined up $$5$$ at a time;

$$2)$$ $$3$$ left over when they lined up $$6$$ at a time;

$$3)$$ $$1$$ left over when they lined up $$7$$ at a time;

$$4)$$ none left over when they lined $$11$$ at a time,

how many soldiers survived the battle?

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