# Extension of lady and monster

A famous problem: a lady is in the center of the circle lake, the monster is on the boundary of the lake. The speed of the monster is $v_m$, of swimming lady — $v_l$. The goal of the lady is to come to the shore without meeting the monster, the goal of the monster — to meet the lady.

If the monster cannot swim, the lady will always win if $\frac{v_m}{v_l} < 4.6033$. If this condition is not satisfied — the monster and the lady will follow the strategies which don't allow them neither win nor lose.

I was thinking about “real-life” extensions of this game (e.g. probabilistic) such that for any fraction of speeds either a lady or a monster can win (with non-zero probability for probabilistic extension). I always get a result that monster will never win. This fact fact is quite sad for the poor monster.

So, I will be happy if you can suggest me a non-trivial extension in which a monster cannot swim but can win (situation when they start at the same point e.g. is trivial).

• After one hour the lady starts getting hungry, after one day she is almost starving and has to get out of the water. Otherwise she dies... – Fabian Apr 6 '11 at 6:59
• Here's the question this builds on: math.stackexchange.com/questions/31097/a-lady-and-a-monster – joriki Apr 6 '11 at 8:09
• What if you assumed the lake was evaporating or being drained and that the woman was standing on an circular island in the middle of the lake . So that as time passes there is less water in the lake changing the difference between the island's radius and the lake's radius. Also after a certain time there will be no water and the monster wins. – Kate Apr 6 '11 at 8:15
• @Kate that depends if the monster is able to move on land. There are plenty of mosters that do well swimming but move slowly on land. – yiyi Jan 20 '13 at 7:27
• Shouldn't the lady dive under water, take a random direction and swim in a straight line to the shore, this would maximize her chances that the monster has not chosen the same direction and would be at the same location as hse does when climbing out of the water. – Pascal P Jun 25 '17 at 11:21