19. There are 11 consecutive natural numbers, the sum of the largest and smallest of which is 90. Fill these 11 numbers into the circles in the figure below, with one number in each circle, so that the sum of the numbers in the six circles of each regular hexagon is the same. What is the minimum value of this sum?
【Analysis】From the sum of the largest and smallest numbers among 11 consecutive natural numbers being 90, we can determine that these 11 numbers are from 40 to 50. To achieve the smallest sum, the number that is counted twice in the middle should be as small as possible, the smallest being 40, and the smallest sum would be $(40+41+\cdots+50+40) \div 2=267$, which is not an integer, and thus not possible. Consider the middle number to be 41, the sum would be $(40+41+\cdots+50+41) \div 2=268$. The arrangement can be as follows, but it is not unique.