I've got an idea: swim. Or put floating barrels on the water with the 9.5m planks firmly attached so they float atop the barrels. By attaching 10 or 20 in a row, you could safely walk across the middle without falling over.
Another solution I've actually done:
Place one board so it's sticking out 1.5 meters over the edge. It has 8 meters still on flat ground. Now, have 1 man stand on the end furthest from the moat. Because of mechanical advantage, you can put the weight of ~5.33 men on the other end of the board (8 / 1.5 ~= 5.33 ). Carry a board vertically 1 meter out, then drop the top end so it swings down and lands on the opposite edge. Set the close edge so .5 meters of the second board is resting on the first board, and there will be .5 meters resting on the opposite side, with the remaining 8.5 meters bridging the gap. I'm not sure of the exact physics, but I know that the maximum mechanical disadvantage for the guy holding the board down is 10:8, or 1.25, and that would occur when someone was standing at the very opposite edge of the moat. So 2 guys on the end away from the castle would be sufficient for 1 guy to cross the bridge.
Once the first guy is across, you have a few options:
1. Send a second guy across (total of 4 guys), reverse the boards (so the far board has 1.5m sticking over the moat and the near board covers the remaining 8.5 meters), then walk the remaining 2 guys across, bringing the second board with them. (This is the method I used, because the objective was to cross the gap and bring the boards with us so we could cross the remaining gaps.)
2. Pull both boards so that .75 meters are sticking over the moat and use a 3rd board to cover the remaining 8.5 meters. Now, you have a worst case advantage of 1.75:1, because you have 8.75 meters on land, and if the load is more than 5 meters from your edge, the other board is taking the extra load. (This is basically the same setup as Skumbag's, except I'm using weight instead of lashing to keep things from falling.)
3. Pull both boards so 5 meters is over the moat and the remaining 4.5 meters is on dry land on either edge. The disadvantage is now 1.11:1, so 1 big guy holding some heavy-ish stuff could get smaller guys across.
You could also put something very heavy on the end to support more than 2 people crossing at a time (such as an anvil or large tank filled with water). Your wieght-over-the-water would ultimately be limited by how much stress the boards could take, but you could always roll heavier objects across multiple boards at once to distribute the load.
The disadvantage of my method is the requirement to leave something heavy on the ends while people are crossing, but it has the advantage that the army can breach the gap anywhere along the moat. I would guess that for any reasonable army, the advantage would far outweigh the disadvantage. Of course, I'd also guess that a reasonable army could make 10+ meters boards.
Note: Umm. I made a mistake in my counting somewhere, and don't feel like fixing it at the moment. However, the concept remains valid. Edit: the mistake is on the picture, frame 4. It should read "8.5 m", not "7.5 m".
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