|The 25 Holes Challenge|
Leaving holes within a stable matrix of pieces is a time-honored puzzle challenge, from coin arrangements to the 3D tower of Jenga. We can investigate what is the maximum number of holes that still preserves a rigid structure of the remaining pieces, so none can slide or move about, and what arrangement of pieces can yield any given number of holes. You could relate this to maze building, road systems, housing developments, Swiss cheese, and even scheduling of appointments.
Your challenge for this 25th Anniversary feature is to find as many solutions as possible for leaving 25 holes in a tiling of Vee-21 pieces. For each new solution we receive, we'll award a silver dollar, up to 25 distinct solutions. The holes may be single unit openings or larger groupings of spaces, or any combination of these. The sample above shows a 16-holer solution.
The only requirement is that all the pieces must be locked in place by their neighbors, so none will slide if the board is tilted. Oh, and while you're at it, no two of the same color should share sides. Here are the solutions identified so far. Arrangements that are trivial variations of these do not count as different.
Bonus question: Solutions are known to exist for Vee-21 with all these holes: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 and 43. If you can find a stable arrangement with 37 and 40 holes, or prove them impossible, you will win a separate prize. The tentative solution with 37 holes, shown below, is by Pete Rudnick.
This contest is still open! Email your solutions in electronic form to: The 25 Holes Challenge or as a drawing on paper to:
Kadon Enterprises, Inc.
There is no deadline. This contest will continue in effect until all 25 silver dollars have been claimed. Happy puzzling!
||25th Anniversary index|