Timeline for Making perpetual motion machine from candy-sharing cats
Current License: CC BY-SA 4.0
26 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2023 at 15:16 | comment | added | Eric | @AnttiP Surprisingly, there exists a 13-pmm. Check the new answer in the puzzling-stackexchange link at the end of the question. | |
| Jun 8, 2023 at 10:05 | review | Close votes | |||
| Jun 8, 2023 at 12:43 | |||||
| S May 31, 2023 at 16:07 | history | bounty ended | CommunityBot | ||
| S May 31, 2023 at 16:07 | history | notice removed | CommunityBot | ||
| May 28, 2023 at 10:09 | comment | added | AnttiP | For each permutation I only considered initial candy distributions where cat #M shares (thus for each permutation there are only (M-1)! possible distributions). Also I used bitwise operations and multi-threading but it still took 12 hours. I have some ideas on how to prune the search space further. For example it seems that cats #M and #M-1 can always be swapped, though I have no idea why this is the case. Also permutations like 354789612 can be discarded because if cat #3 receives a candy then cat #5 also gets one which implies that cat #5 will eventually have 6 candies. | |
| May 28, 2023 at 9:56 | comment | added | Eric | @Anttan A suggestion towards finding large PPMs: the number of total candies in a PPM seems to hover around $M(M+1)/4$ (floor). Can you try searching for this number of candies? | |
| May 28, 2023 at 8:50 | comment | added | Eric | @AnttiP Thanks, this really seems to suggest that PMMs exist when M is even. Did you use any tricks to speed up the search? | |
| May 28, 2023 at 7:47 | comment | added | AnttiP | Just finished a computer search, there are no 11-PPMs | |
| May 27, 2023 at 12:02 | comment | added | AnttiP | There are definitely 10-PPMs. In fact, here's an exhaustive list of all PPMs with M<11. | |
| May 24, 2023 at 6:52 | comment | added | Per Alexandersson | @Eric, so that at least one among the n cats, at least one always has at least n candies. | |
| May 23, 2023 at 23:39 | comment | added | Eric | @PerAlexandersson What do you mean by the average number of candies? | |
| May 23, 2023 at 19:50 | comment | added | Per Alexandersson | What if the average number of candies exceeds the number of cats? | |
| May 23, 2023 at 16:19 | comment | added | Peter Taylor | That was a dichotomy. If it's "exactly" then that creates a lot of blocking states and may simplify the analysis; if it's "at least" then I would be inclined to consider whether a starting state assigning $n^3$ to each of them would work. | |
| May 23, 2023 at 16:19 | comment | added | Eric | @JoeSilverman Joe, when you encounter cats who share candies among themselves, you know you've met no mortals! "Since there are many algorithms for which this is an interesting question" Are you referring to cats sharing candies using different rules (algorithms) by this claim? I wonder why should many general questions about these algorithms be interesting/difficult. What do they have in common? | |
| May 23, 2023 at 15:32 | comment | added | Eric | @PeterTaylor Exactly. | |
| May 23, 2023 at 15:15 | comment | added | Joe Silverman | Amusing name for the puzzle, although to justify it, you really should say that you're working with sets of immortal cats. :) In more prosaic terms, if I've understood correctly, you've described an algorithm and are calling it a "perpetual motion machine" for a certain input if the algorithm never terminates. Since there are many algorithms for which this is an interesting question, you might add some modifiers to your abbreviation, e.g., CSCPMM (Candy Sharing Cats Perpetual Motion Machine). | |
| May 23, 2023 at 15:07 | comment | added | Peter Taylor | Is the condition in step 1 that cat $n$ has exactly or at least $n$? | |
| May 23, 2023 at 14:39 | history | edited | Eric | CC BY-SA 4.0 |
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| S May 23, 2023 at 14:39 | history | bounty started | Eric | ||
| S May 23, 2023 at 14:39 | history | notice added | Eric | Canonical answer required | |
| May 19, 2023 at 14:21 | history | edited | Eric | CC BY-SA 4.0 |
Updated the progress
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| May 19, 2023 at 6:16 | comment | added | Eric | @DominicvanderZypen You're welcome, Dominic! The current known results are obtained more or less by brute force search, which becomes infeasible for more than 10 cats. | |
| May 17, 2023 at 16:35 | comment | added | Dominic van der Zypen | Fantastic riddle, thanks Eric for sharing it!! | |
| May 17, 2023 at 15:58 | history | edited | Eric | CC BY-SA 4.0 |
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| May 17, 2023 at 15:41 | history | edited | Eric | CC BY-SA 4.0 |
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| May 17, 2023 at 15:27 | history | asked | Eric | CC BY-SA 4.0 |