Tuesday, August 16, 2005

The Plane in the Wind

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It traverses with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less, or the same if, throughout both flights, at the same engine speed, a costant wind blows from A to B?

Monday, July 04, 2005

Back with a bang :)

Manupulative codewords - Hofstadter's MIU system

This system of codewords have only stings of letters formed from the alphabets, M, I, U with MI as one of the codewords. You can form other codewords in the system by the following four rules :

x in the below lines can be any string of letters from M, I, U that makes a codeword in each of the rules.

1. If xI is a codeword, then xIU is also a codeword.
2. If Mx is a codeword, Mxx is also a codeword.
3. In any codeword, III can be replaced by U.
4. In any codeword, UU can be omitted.

Questions : Show that MUII is a codeword. Is MU a codeword?