In regular chess no piece can checkmate the opposite king alone (i.e. without the help of his allied king). But a [Maharajah](http://en.wikipedia.org/wiki/Maharajah_and_the_Sepoys "Maharajah") can. 

* Is there a piece weaker than the Maharajah, of course invented, that can **force** checkmate on the opposite king alone?
* Is there a piece weaker than the Maharajah, of course invented, that can checkmate the opposite king alone (but optimal play from the opposite king can hold a draw)?

To calculate the power of a piece: 

1. Take sum of squares attacked in all corners as $x$,
2. Number of squares attacked when in any of 4 centre squares as $y$.
3. The power of the piece is then $\frac{x+y}{5}$

For example the bishop: $7 \times 4$ for the corners, $13$ for the centre. $\frac{28+13}{5} = 8.2$

A piece is weaker than another if its power is lower.