The number of soldiers is 1073. Form a 3-person ***x platoon; 5 people ***y row; 7 people ***z row; (Neither is a remainder). Then * * * Number of people: 3x+2=5y+3=7z+2. Namely: {3x-5y =1; 5y7z =- 1； 3x = 7z three equations, plus the constraint of1000 < 3x+2 <1100 (derived from the condition that the Han army also suffered 400 ~ 500 casualties), we get: x = 357y = 214; z = 153； Then the number of soldiers is 3x+2=3*357+2= 1073.

Han Xin pointed to the soldiers:

In Sun Tzu's Art of War more than a thousand years ago, there was such an arithmetic problem: "Today's events are unknown, and the number of three and three leaves two, the number of five and five leaves three, and the number of seven and seven leaves two. What is the geometry of things? " According to today's words: divide a number by 3 and 2, by 5 and 3, by 7 and 2, and find this number. This kind of problem, some people call it "Han Xin points soldiers". A kind of problem is formed, that is, the solution congruence in elementary number theory.