MathDB

Consider the set

S = \{1,2,3, ...,1441\}

. 1. Nora counts thoses subsets of

S

having exactly two elements, tbe sum of which is even. Rania counts those subsets of

S

having exactly two elements, the sum of which is odd. Determine the numbers counted by Nora and Rania. 2. Let

t

be the number of subsets of

S

which have at least two elements and the product of the elements is even. Determine the greatest power of

2

which divides

t

. 3. Ahmad counts the subsets of

S

having

77

elements such that in each subset the sum of the elements is even. Bushra counts the subsets of

S

having

77

elements such that in each subset the sum of the elements is odd. Whose number is bigger? Determine the difference between the numbers found by Ahmad and Bushra.

Problem Statement