Week 7: Wednesday
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Q1. (35)

Goldbach, a mathematician, conjectured that every even integer greater than 2
is a sum of two primes. Write a program to verify the conjecture till the
number 50. That is, for every even number greater than 2 up to 50, either
express it as a sum of two prime numbers, or show that it cannot be expressed
as such a sum.

(You may use an array to store all primes. You may also use a function to
express a number as sum of two other numbers. You can do it in your own way as
well.)

Q2. (65)

Consider a 8x8 matrix. Initially each entry of the matrix is coloured black or
white. Next, the matrix is divided into 4 equal square matrices (of size 4x4).
The colour of all entries of the 1st (i.e., top-left) and the 4th (i.e.,
bottom-right) matrices are flipped while those of the other two remain as is.

This process is repeated recursively for all the 4 sub-matrices, where each one
of them is again divided into 4 sub-matrices, of which the colours of the 1st
and 4th are flipped, and so on. The process is continued till it cannot be
broken into any sub-matrix, i.e., when the matrix is of size 1x1.

Write a program to implement it.

Assume that all the entries of the 8x8 matrix are black to start with. Print
the final configuration.

(Use 0 to signify black, and 1 to signify white.)