Hello Ed,

I don't believe that writing a program to test all possible combinations is
"clever", but nonetheless, I have done so, and no solution is possible.  The
below program, written in matlab, runs to completion, with no combination of
11 squares possible.

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function knights

conns = zeros(64,13);
for a=0:63
	b=floor(a/8);
	c=mod(a,8);
	conns(a+1,1) = mod(b-2,8)*8+c +1;
	conns(a+1,2) = mod(b-1,8)*8+mod(c-1,8) +1;
	conns(a+1,3) = mod(b-1,8)*8+c +1;
	conns(a+1,4) = mod(b-1,8)*8+mod(c+1,8) +1;
	conns(a+1,5) = b*8+mod(c-2,8) +1;
	conns(a+1,6) = b*8+mod(c-1,8) +1;
	conns(a+1,7) = a +1;
	conns(a+1,8) = b*8+mod(c+1,8) +1;
	conns(a+1,9) = b*8+mod(c+2,8) +1;
	conns(a+1,10) = mod(b+1,8)*8+mod(c-1,8) +1;
	conns(a+1,11) = mod(b+1,8)*8+c +1;
	conns(a+1,12) = mod(b+1,8)*8+mod(c+1,8) +1;
	conns(a+1,13) = mod(b+2,8)*8+c +1;
end

knightpos = 1;
avail = ones(1,64);
avail(conns(1,:))=0;

success = placeknight(knightpos,avail,conns);


function success = placeknight(knightpos,avail,conns)

success=0;

if length(knightpos)==11
	success=1;
	knightpos
	return
end

for a=find(avail)
	newknightpos=[knightpos,a];
	newavail=avail;
	newavail(1:a-1)=0;
	newavail(conns(a,:))=0;
	if length(newknightpos)==3
		disp(newknightpos);
	end
	success = placeknight(newknightpos,newavail,conns);
	if success==1
		return
	end
end

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Sincerely,
Brian Galebach