CSE Blog - quant, math, computer science puzzles

Source: Discussions with BX Mumbai team on my flight from New York to Mumbai Problem: The flight from New York (Newark - EWR) to Mumbai (Bombay - BOM) takes the aerial route as shown in the figure. Why do the flights not take straightline distance to minimize cost? Hint: The answer is mathematical. Do not think of regulatory or political reasons. Update:  (19-07-2012) Assume earth is perfect sphere 

Source: Asked to me by Sumit Yadav Problem: Is it possible to label the edges of a cube using the numbers 1 through 12,  in such a way that the sums of the numbers on any two faces of the cube are equal? Update: (19-07-2012) Solution posted by Rakesh Roy (SAP Labs, Bangalore) and Praveen Reddy Vaka (Mechanical Engg IITM Alumnus 2006, CSE IIT Kanpur Alumnus 2011) in comments!