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22f53be42d Sturmian edits
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2026-03-15 08:01:45 -07:00
7cb1f04fb4 Retrograde edits 2026-03-15 08:01:40 -07:00
3 changed files with 3 additions and 4 deletions

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@@ -49,7 +49,6 @@ Have an instructor check your solution.
(0) edge (2) (0) edge (2)
(2) edge (3) (2) edge (3)
(2) edge[bend left] (4) (2) edge[bend left] (4)
(4) edge[bend left] (2)
(3) edge (1) (3) edge (1)
(4) edge (3) (4) edge (3)
(4) edge[loop right] (4) (4) edge[loop right] (4)

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@@ -375,7 +375,7 @@ Construct a minimal Sturmain word of order 5.
\problem{} \problem{}
Argue that the words we get by \ref{sturmanthm} are minimal Sturmain words. \par Show that the words we get by \ref{sturmanthm} are minimal Sturmain words. \par
That is, the word $w$ has length $2n$ and $\mathcal{S}_m(w) = m + 1$ for all $m \leq n$. That is, the word $w$ has length $2n$ and $\mathcal{S}_m(w) = m + 1$ for all $m \leq n$.
\begin{solution} \begin{solution}

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@@ -252,7 +252,7 @@ It is Black's move. Can Black castle? \par
\difficulty{2}{5} \difficulty{2}{5}
Neither Black nor White captured a piece on their last move. \par Neither Black nor White captured a piece on their last move. \par
It is Black's move. Can he castle? \par It is Black's move. Show that he cannot castle? \par
\hint{What was White's last move? Check the cases.} \hint{What was White's last move? Check the cases.}
\manyboards{ \manyboards{
@@ -348,7 +348,7 @@ It is White's move. What was the previous move?
Bc8, Bc8,
pg6, pg6,
Pg5,kh5, Pg5,kh5,
Pd4,Qg4,Bh4, Pd4,qg4,bh4,
pd3, pd3,
Pd2,Be2,Bg2, Pd2,Be2,Bg2,
Nc1,rd1,Ne1,Kf1,Qg1,Rh1 Nc1,rd1,Ne1,Kf1,Qg1,Rh1