RE: n-Queens Problem

David Carlisle wrote a very cool:

… solution that works for
    any size chessboard …

Thank you David!

Here is how David models the chessboard:

<n-queens>
    <queen column="1" row="3"/>
    <queen column="2" row="1"/>
    <queen column="3" row="4"/>
    <queen column="4" row="2"/>
</n-queens>

And here is his (mind-blowing) Schematron schema:

<sch:schema xmlns:sch="http://purl.oclc.org/dsdl/schematron"
                      queryBinding="xslt2">
   
    <sch:pattern id="n-Queens-Problem">
       
        <sch:rule context="n-queens">
            <sch:assert test="every $c in 1 to count(queen) satisfies exists(queen[@column=$c])">
                There cannot be two queens in the same column.
            </sch:assert>
            <sch:assert test="every $r in 1 to count(queen) satisfies  exists(queen[@row=$r])">
                There cannot be two queens on the same row.
            </sch:assert>
            <sch:assert test="count(queen)=count(distinct-values(queen/(number(@row) - number(@column))))">
                There cannot be two queens on a (falling) diagonal.
            </sch:assert>
            <sch:assert test="count(queen)=count(distinct-values(queen/(number(@row) + number(@column))))">
                There cannot be two queens on a (rising) diagonal.
            </sch:assert>
        </sch:rule>
    </sch:pattern>
   
</sch:schema>