Timeline for "Lamp-switch set-up number" of $n$ [closed]
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2022 at 19:15 | history | closed |
Andreas Blass Gro-Tsen domotorp Mark Wildon Daniele Tampieri |
Not suitable for this site | |
| May 16, 2022 at 9:19 | vote | accept | Dominic van der Zypen | ||
| May 15, 2022 at 12:36 | answer | added | Roland Bacher | timeline score: 1 | |
| May 15, 2022 at 9:46 | comment | added | Dominic van der Zypen | Right - I am wrong, sorry | |
| May 15, 2022 at 8:05 | comment | added | Fedor Petrov | hm, why do not they commute? | |
| May 15, 2022 at 7:52 | comment | added | Dominic van der Zypen | @FedorPetrov, in the sequence $e_1,\ldots, e_m$ you can press any button more than once, and pressing $e$ and $e'$ may not commute | |
| May 15, 2022 at 1:40 | comment | added | Gerry Myerson | So, we have found a complicated description of the identity function. | |
| May 14, 2022 at 17:33 | comment | added | Fedor Petrov | Or, more elementary, if you have $k<n$ buttons, you get at most $2^k<2^n$ combinations of lamps, thus not all. This contradicts to the possibility to switch each separate lamp. | |
| May 14, 2022 at 17:28 | review | Close votes | |||
| May 16, 2022 at 19:15 | |||||
| May 14, 2022 at 17:15 | comment | added | Andreas Blass | Think of $\mathcal P(\{1,\dots,n\}$ as an $n$-dimensional vector space over the $2$-element field. You're asking for the minimal size of a set $E$ whose linear combinations include all the standard basis vectors $\{k\}$. Such an $E$ spans the whole space, so the minimum size is $n$. | |
| May 14, 2022 at 16:39 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |