Consider the 20000 x 20000 sparse matrix,
A=round(sprand(2e4,2e4,1/1e4*100)*1000);
The task is to divide this matrix into 2x2 tiles and to form the reduced 10000 x 10000 matrix B such that B(i,j) is the sum over the elements of (i,j)-th tile of A. For example,
B(1,1) = A(1,1)+A(2,1)+A(1,2)+A(2,2)
B(2,1) = A(3,1)+A(4,1)+A(3,2)+A(4,2)
etc...
Your solution must execute in less than 0.3 sec.
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I find it interesting that I didn't immediately think of the rather obvious method.
I also find it interesting the method I (and ofcourse Matt) used was probably what Matt had in mind while coming up with this problem.