Given the five olympic rings how can the digits one through nine be placed within the nine regions (five non-overlapping ring regions and four overlapping regions shared between two rings) so that each ring contains a successively incrementing total?
Or alternatively, using the labels A through I for the regions, how can the numbers one through nine be assigned to the variables such that:
How many different totals can fit in the first circle? Find a complete solution for each.
Source: Original. Similar to previous POTW July 25, 1997