Stage: 4 Challenge Level:
Christina sent us her solution:
A knight can't make a tour on a $2\times n$ board, for any $n$,
because it must go into and out of a corner square, and it can't do
this without going back on itself.
On the $3\times 4$ grid, we must use a path from the loop JAGIBHJ
and a path from the loop KDFLCEK. But they only link up between J
and C, and between B and K. So the path must start at a neighbour
of J, B, K or C, follow round that loop, switch to the other loop
and follow round that. Obviously the path can go round the loop in
either direction. So there are $16$ possible tours:
Since it's not possible to get from the finish directly back to the
start in any of these tours, there is no circuit.