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Draw a regular hexagon divided into six equilateral triangles.
On each side, place another equilateral triangle, to create a
Can you place the numbers 1-12 into the 12 triangles such that the sum of the five triangles in each of the six lines is the same? (For example, in the figure, BCDEF and GHIJK are two lines of five.)
If it is possible, what are the largest and smallest common sums possible? If it is not possible, how many numbers would you have to change, keeping all 12 unique, to achieve the smallest possible common sum?