Timeline for Covering discrete triangle with generalized knight jumps
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2023 at 6:25 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 19, 2023 at 6:18 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 19, 2023 at 6:12 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 15, 2023 at 18:03 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 15, 2023 at 11:50 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 12, 2023 at 20:49 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jan 12, 2023 at 19:45 | comment | added | Jens Fischer | Yes, this is equivalent to $\dfrac{n(n-1)}{2}$ being divisible by $3$ since there are exactly as many squares in the triangle. | |
| Jan 12, 2023 at 15:30 | comment | added | Peter Taylor | With this modification the triples are always true triples so the number of uncovered squares is divisible by three unless $n \equiv 2 \pmod 3$. Revised solutions for n to 11. | |
| Jan 12, 2023 at 14:39 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 12, 2023 at 13:13 | comment | added | Jens Fischer | Sorry @PeterTaylor , I made a typo in the definition of (now) $\Gamma$. It was meant to be $m\leq n-(l-1)$ and not $m\leq n-l$. Also the third tuple then becomes $(k,n-(l-1))$. The tripple containing $(1,n-1)$ is then $(1,1),(1,2),(1,n-1)$. | |
| Jan 12, 2023 at 13:06 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 12, 2023 at 13:04 | comment | added | The Amplitwist | @WlodAA Related: Did mathcal stop working properly? on MathOverflow Meta. | |
| Jan 12, 2023 at 12:45 | history | edited | Jens Fischer | CC BY-SA 4.0 |
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| Jan 12, 2023 at 12:42 | comment | added | Peter Taylor | In fact, I think that leaving only 1 square uncovered is impossible for any even $n$, so either we're understanding the problem differently or your solution for $n=8$ must be wrong. Observe firstly that $(1, n-1)$ can never be covered; secondly that the number of $(i, 1)$ covered must be even; and thirdly that with $n$ even there are an odd number of $(i, 1)$. | |
| Jan 12, 2023 at 11:59 | comment | added | Peter Taylor | Can you exhibit your solutions for 6, 7, 8? The ones I get using exhaustive search are worse, so I want to see whether it's a bug in my code or a misunderstanding of the problem. | |
| Jan 12, 2023 at 11:11 | comment | added | Jens Fischer | Sure, I can change that | |
| Jan 12, 2023 at 10:35 | comment | added | Wlod AA | Well, I got a small square symbol too just the same. | |
| Jan 12, 2023 at 10:34 | comment | added | Wlod AA | Your mathcal symbols don't work on my screen, all of them show as small square symbols. Possibly, you could use "Delta" $\ \Delta,\ $ or "triangle" $\ \triangle,\ $ or nabla $\ \nabla,\ $ etc. ##### Let me try mathcal myself right here, $\ \mathcal T$ -- will it work properly? | |
| Jan 12, 2023 at 9:55 | history | asked | Jens Fischer | CC BY-SA 4.0 |