In a number system the product of 44 and 11 is 2124. The number 3111 of this system, when converted to the decimal number system,

becomes:

The figure below shows the network connecting cities, A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F?

The sum of 3rd and 15^th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13^th elements of the same progression. Then which element of the series should necessarily be equal to zero?