Answers.Body: <p>Here are my attempts for Q and N.</p>
  <p><a href="https://i.sstatic.net/vg7FP.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vg7FP.png" alt="Q record?" /></a></p>
  <p>Observe that I didn't use g&amp;h at all, maybe 11 are possible after all.</p>
  <p><a href="https://i.sstatic.net/Fcu0O.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Fcu0O.png" alt="N record?" /></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-04-28T18:30:30.277Z
Answers.LastActivityDate: 2023-04-28T18:30:30.277Z
Answers.UserDisplayName: Hauke Reddmann
Body: <p><a href="https://i.sstatic.net/uJkoK.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/uJkoK.jpg" alt="Rook Roundtrip" /></a></p>
  <p>In the picture, you see the longest roundtrip of a rook such that there are no &quot;shortcuts&quot; - imagine the target squares are given, then at each square you have exactly two other given squares accessible to the rook, and they connect to a round trip. (Trivially the longest rook trip length is 2*8.)</p>
  <p>What are the values for the other officers? Q and N are most interesting. (I think I know the maximum for N.)</p>
  <p>Note: a1-b1-c1 is forbidden, even if you can't go from a1 to c1 if something stands on b1.</p>
  <p>Son of Note: You <em>could</em> formulate this problem far simpler: &quot;Place m queens (knights,...) such that all queens are protected twice&quot;. But it's not the same problem anymore - the Qa6 will never &quot;touch&quot; Qh3.</p>
  <p><a href="https://i.sstatic.net/OUV20.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OUV20.jpg" alt="Not a roundtrip" /></a></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-04-26T06:42:33.567Z
Comments.Text: Can you explain the details further? Maybe with some small examples.. I couldn't understand what is a "roundtrip".
Comments.UserDisplayName: Minot
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-04-26T08:09:42.287Z
Comments.Text: @Minot you are looking for a cyclic list of squares such that (i) each pair of consecutive squares is a [queen's] move apart, and (ii) no non-consecutive pair is a [queen's] move apart.
Comments.UserDisplayName: Especially Lime
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-04-26T10:41:12.310Z
Comments.Text: Queen looks to be 10 but I can't prove it
Comments.UserDisplayName: Andrew Chin
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-04-26T18:07:27.517Z
Comments.Text: @AndrewChin: Ditto. (A computer search will take...long :-)
Comments.UserDisplayName: Hauke Reddmann
Tags: <problems><records><mathematics>
Title: Roundtrips with no shortcuts
ThreadText: # Roundtrips with no shortcuts
  
  (Asked by: username_0 on 2023-04-25)
  
  [![Rook Roundtrip](https://i.sstatic.net/uJkoK.jpg)](https://i.sstatic.net/uJkoK.jpg)
  
  In the picture, you see the longest roundtrip of a rook such that there are no "shortcuts" - imagine the target squares are given, then at each square you have exactly two other given squares accessible to the rook, and they connect to a round trip. (Trivially the longest rook trip length is 2\*8.)
  
  What are the values for the other officers? Q and N are most interesting. (I think I know the maximum for N.)
  
  Note: a1-b1-c1 is forbidden, even if you can't go from a1 to c1 if something stands on b1.
  
  Son of Note: You *could* formulate this problem far simpler: "Place m queens (knights,...) such that all queens are protected twice". But it's not the same problem anymore - the Qa6 will never "touch" Qh3.
  
  [![Not a roundtrip](https://i.sstatic.net/OUV20.jpg)](https://i.sstatic.net/OUV20.jpg)
  
  **Tags:** problems, records, mathematics
  
  > **Comments:**
  > **username_1**: Can you explain the details further? Maybe with some small examples.. I couldn't understand what is a "roundtrip".  
  > **username_2**: @username_1 you are looking for a cyclic list of squares such that (i) each pair of consecutive squares is a [queen's] move apart, and (ii) no non-consecutive pair is a [queen's] move apart.  
  > **username_3**: Queen looks to be 10 but I can't prove it  
  > **username_0**: @AndrewChin: Ditto. (A computer search will take...long :-)  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_0 on 2023-04-28. Score: 1
  
  Here are my attempts for Q and N.
  
  [![Q record?](https://i.sstatic.net/vg7FP.png)](https://i.sstatic.net/vg7FP.png)
  
  Observe that I didn't use g&h at all, maybe 11 are possible after all.
  
  [![N record?](https://i.sstatic.net/Fcu0O.png)](https://i.sstatic.net/Fcu0O.png)
  
  
  ---
  
  