These questions are based on a puzzle that new contributor Stanley Wu-Wei Liu picked up from WeChat and translated from Chinese for us. Your friend tells you that they have placed the six numbers 2, 3, 4, 5, 6, and 7 in the circles in the diagram in the figure to the left so that the sum along any side of the triangle is the same. However, based just on this information, there is no way for you to know what that common sum is. (That’s because there are different solutions with different sums — can you find them?)
- Is there a set of six integers your friend could use instead so that there is at least one solution, and all of the solutions have the same common sum along the sides?
- Is there a set of six integers so that there is exactly one solution, period? (Such that all three sides have the same sum.) For this part, you should not consider rotations or reflections of the filled-in diagram as different. Note that a positive answer to this part (b), if it turns out to be possible, would immediately give an answer to part (a).