Source: Asked to me by Ram Kumar, a frequent visitor to this blog.
There's a duck swimming in a circular lake with a wolf at the edge. wolf won't enter water. Duck in water is slower than Wolf on land. Duck on land is faster than the Wolf on land. Given the lake diameter 'd' and wolf speed 'w', what is the minimum speed of the duck in water so that he can escape? what should be his escape strategy?
1) Its less than w/4.
2) There is pi involved. :)
Answer given by Vivek Jha (EE, IITB) in the comments. Proof of the solution given by me in the comments of one of the earlier posts: http://pratikpoddarcse.blogspot.com/2009/11/polyas-urn-problem.html?showComment=1258400372028#c8784580092886919079