Castle -
A square medieval castle on a square island was under siege. All around the island, there was a 10 metre wide water moat. But the conquerors could make foot-bridges only 9.5 metres long. Nevertheless a wise man was able to figure out how to get over the water. What do you think was his advice?
(There's a place on the other side to put the bridge against, not just a sheer wall. the water moat has square corners - that section of the moat is about 14.1 metres wide.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Castle - solution
You can put one foot-bridge over one corner (thus a triangle is created). Then from the middle of this foot-bridge lay another foot-bridge to the edge (corner) of the castle. You can make a few easy equations confirming that this is enough.