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Two sides of mathematics
First of all, it is a coincidence that you used the method of 576-5 12=64.

Solution: There are lights at the three points A, B and C on the bridge and the midpoint between the two points. The distance between each light should be equal, and at least how many lights should there be. In fact, it is to find the greatest common divisor of 576 and 5 12. The greatest common factor is 64, and their midpoints are 288, 256, 288, 256, all multiples of 64, so 64 meets the conditions.

(576+512) ÷ 64+1=18 (lamp) Both sides: 18×2=36 (lamp).

(Find how many intervals the greatest common factor equals with the total length, plus a lamp at point A is the answer on one side.)