Candle Swap

This CAD model was designed by Oskar van Deventer, copyright (c), 14 July 2024.

Candle Swap was inspired by a classic candle design. When seeing the candle with friends, it has to be turned into a puzzle. The idea was obvious: add gears and swap the candles to get them into a particular order. The puzzle plays like a twisty puzzle. Each turn swaps two or three pairs of candles. The object is to scramble the puzzle, and then sort the candles in order. One order is low to high. Another order is sorted by color, with the highest in the middle. A conjecture is that any order of candles is possible to achieve. Why is that?

Eitan Cher provided the following additional information: "Menorah" technically refers to a candelabrum with 7 candles. That's what was in the temple that the Greeks destroyed. The candelabrum used on Hanukkah is called a Hanukkiah, and it has 9 candles: 8 of them represent the miraculous 8 days that the small amount of oil lasted, and the 9th is the one used to light the rest.  That one is called the "shamash" and it is always supposed to be situated higher than the other 8.

Jaap Scherphuis provided a full analysis of the puzzle. The puzzle has 362880 (9 factorial) states. Any state can be reached from any other state in 23 moves. From any state, there are 46 "antipode" states that are 23 moves away.

Here are some links about this design.
https://www.youtube.com/watch?v=-oh7ZpTWZn0
https://i.materialise.com/en/shop/item/candle-swap
https://www.shapeways.com/product/4Y8D7Y7AZ/candle-swap
https://i.materialise.com/forum/t/candle-swap-by-oskar/3808
https://twistypuzzles.com/forum/viewtopic.php?t=39861

Feel free to 3D-print an extra sample to give to a friend, as long as you mention the designer and don't charge money.

If you are planning to sell some samples, then please contact me for a license agreement. The royalty fee is 10% of your selling price.

Please do not upload the design to a commercial service, or redistribute the design in any way other than linking to the YouTube video: https://www.youtube.com/watch?v=-oh7ZpTWZn0

Enjoy!

Oskar
25 December 2024

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Analysis by Jaap Scherphuis

Moves:
A (2 1)(4 3)(7 6)
B (3 2)(6 5)(9 8)
C (5 4)(8 7)

Position: 987654321
Solution: BABABA CABCABCAB  ACABCB

depth 1, positions 3, total 4
depth 2, positions 6, total 10
depth 3, positions 12, total 22
depth 4, positions 24, total 46
depth 5, positions 48, total 94
depth 6, positions 94, total 188
depth 7, positions 184, total 372
depth 8, positions 362, total 734
depth 9, positions 685, total 1419
depth 10, positions 1280, total 2699
depth 11, positions 2399, total 5098
depth 12, positions 4467, total 9565
depth 13, positions 8271, total 17836
depth 14, positions 14926, total 32762
depth 15, positions 25950, total 58712
depth 16, positions 42555, total 101267
depth 17, positions 63294, total 164561
depth 18, positions 78867, total 243428
depth 19, positions 70977, total 314405
depth 20, positions 37616, total 352021
depth 21, positions 9758, total 361779
depth 22, positions 1055, total 362834
depth 23, positions 46, total 362880

The 46 antipodes:
123798546
123879465
126495837
128463975
132798654
132987465
135264987
142635987
143256987
145238967
145328697
149265783
149265873
154237968
175634289
184365927
213548769
213857649
214689735
214869375
217395846
218394756
231475896
231854976
234157986
235148976
236198574
237418965
243175968
243579816
312469578
312659847
321549876
321694785
321976584
321978564
327149586
412359687
412539867
412973865
413268597
421579386
432765189
512498367
732165489
813249576


Contact: 
https://oskarvandeventer.nl/index_contact.php?subject=Print%20It%20Yourself


