Timeline for Can you irrigate your lawn with 23 sprinklers?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 24, 2021 at 19:28 | comment | added | ErikE | Comparing your answer to the accepted answer, it seems that your intuition about using symmetry to simplify the problem was good, the only difference being that the accepted answer's symmetry began in the center. While it's surprising that the solution uses 7 circles around the center one instead of 6 (which perfectly tiles a plane), it makes sense when you realize that increasing the number of 2nd-ring circles makes the second ring take up more space, so the outer ring's circles (being placed sequentially in a jagged formation) finally touch without leaving any gaps. | |
| Jun 24, 2021 at 11:08 | comment | added | Floris | I understand that - but if twelve of the thirteen are a bit closer to the center and the thirteenth is “making up the gap” (or perhaps there are two gap fillers) the fact that the others are closer to the center may help fill the remaining space with one fewer sprinkler… | |
| Jun 24, 2021 at 1:33 | history | edited | AxiomaticSystem | CC BY-SA 4.0 |
thanks, Bass
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| Jun 24, 2021 at 1:33 | comment | added | AxiomaticSystem | @Floris Circular symmetry was the starting point I used to do some initial guesswork and cut down on the number of free variables. The argument for at least 13 in the perimeter doesn't depend on it at all. | |
| Jun 23, 2021 at 16:54 | comment | added | Floris | You are assuming that the outer ring must be circularly symmetrical, but there's no rule that says their centers all need to be the same distance from the center of the big circle. Once you relax that constraint, things may work better for you? | |
| Jun 22, 2021 at 15:44 | comment | added | Bass | when you say "longer", you probably mean "shorter" :-) | |
| Jun 22, 2021 at 15:35 | history | answered | AxiomaticSystem | CC BY-SA 4.0 |