Peter's Non-flipping Tri-Cairos (Exchange Puzzle IPP 25)

“Peter’s Non-flipping Tri-Cairos”

This puzzle is a exchange puzzle by Peter Knoppers for the International Puzzle Party 25 held in Helsinki, Finland 2005

About the puzzle:

Cairos are pentagonal shapes with five equal-length sides and two non[1]adjacent 90-degree angles. Poly-Cairos are – of course – groups of Cairos that share one or more edges. Dieter Gebhardt has written an article about these shapes in CFF 58, pp 15-17. There are 5 tri-Cairos when flipping is permitted, 8 when it is not. This puzzle consists of these 8, two mono-Cai[1]ros and a tray. One of the first things I designed was a mechanical way to prevent flipping by adding a pin near the center of gravity. It also made the pieces much easier to handle and could be used in many other puzzles…

Most of the development time of this puzzle went into the design of a suit[1]able tray. I wanted the tray to be symmetrical (but not all solutions) and have a reasonably short outline. I took a set of tri-Cairos to the Gathering for Gardner and IPP24 in 2004 to discuss this problem with other puz[1]zlers. That didn’t help much. The first suitable tray that actually had a so[1]lution can be obtained from the current one by putting the mono-Cairos at positions 1 and 2. The second working design has the mono-Cairos at positions 1 and 25. Then I realized that adding two mono-Cairos to the set could combine these and result in a tray that was much more symmetri[1]cal. Initially I had a limited set of allowed positions for the mono-Cairos, but I removed that restriction in the final design. The storage solution and many others were found using Andreas Röver’s BurrTools program. This program sometimes finds two solutions that should be counted as one.

Objective / Description:

1. Fit all 10 pieces in the tray (about 80 solutions)

2. Put the mono-Cairos at fields 1 and 3 (2 solutions)

3. Put the mono-Cairos at fields 1 and 4 (2 solutions)

4. Put the mono-Cairos at fields 1 and 22 (1 solution)

5. Put the mono-Cairos at fields 1 and 25 (1 solution)

6. Put the mono-Cairos at fields 3 and 5 (1 solution)

7. Put the mono-Cairos at fields 12 and 15 (1 solution)

8. Put the mono-Cairos at fields 13 and 14 (1 solution)

9. Find other locations for the mono-Cairos that result in only 1 Solution

Packaging: Paper box and zip lock bag

Preliminary estimate of shipping costs from the Netherlands.

Netherlands: from 0 - 10 kg approx $ 12.00

Europe 1: from 0 - 2 kg approx $ 21.00 to Belgium, Denmark (excl. Faroe Islands and Greenland), Germany, France, (incl. Corsica and Monaco), Italy (excl. San Marino and Vatican City), Luxembourg, Austria, Spain (incl. Balearic Islands, excl. Canary Islands), Sweden.

Europe 2: from 0 - 2 kg approx. $ 27.00 to all other countries in Europe (excl. Russia).

ROW (rest of the world): from 0 - 2 kg approx. $ 37.00 – to all other countries (incl. Russia).

The final shipping cost will be determined when the item is closed.

And if more items are sold to the same address, the average shipping cost per item will be lower.