The STAR-9 CHALLENGE

designed by Kate Jones as a gift for
the attendees of the 9th Gathering for Gardner,
Atlanta, GA — March 24-28, 2010
 

The Star-9 Challenge uses a 9-pointed star and digits 1 through 9. Puzzlers are asked to cut out the numbers provided and place them on the points of the star to solve several puzzle tasks.
 

 
The challenge offered here uses a 9-pointed star drawn with a continuous series of straight lines. Each point of the star has a circle connected to four other circles. Arrange the nine numbers in those circles to meet the following conditions:

1. Arrange the numbers in the circles around the star so that a maximum of neighboring pairs have the same sum [easy].

2. Arrange the numbers in the circles so that every group of four circles connected to a given number adds up to a different sum. There will be 9 different sums. Do not add in the number itself to which they are connected.

3. Solve problem 2 so that the 9 sums have the longest string of consecutive integers.

This challenge appeared in the New York Times Numberplay section on December 29, 2014, and you can play it online with their "gizmo" app that figures the sums for you.

A related star pattern appears in our strategy game StarSlide, with 13 circles and 12 game pieces that slide along the lines.