Sudoku puzzle

Okay, puzzle addition: Sudoku puzzle. Available in lot many variations, in easy and medium difficulty levels. Enjoy!

Divisors problem (one more)

Here is a problem w.r.t divisors: For a given positive integers B and X find the number of positive integers N such that number N*X has at least one divisor D such that N < D <= B (Courtesy: www.codechef.com).

The number N, can be represented as a function of B and X, namely f(B, X). Prove the following:

f(B, 1) = 0
f(B, 2) = Floor(B / 2)
f(B, 3) = 2 * Floor(B / 3) - Floor(B / 6)
f(B, 4) = Floor(B / 2) + Floor(B / 4) - Floor(B / 6)
f(B, 5) = 4 * Floor(B / 5) - Floor(B / 10) - Floor((B + Floor(B / 15)) / 8) - Floor((B + Floor(B / 20)) / 7)

Spanish and French architectures

I was looking at some pictures and magazines, where photos of some spanish villas, and french houses and articles are there. From those, I think spanish and french architecture styles are along these lines.

French use hues of pink, olive green and brown heavily. French windows are long and sleek. Spanish villas typically use terracotta bricks heavily. Windows are characterized by moorish arches, less-height, fat (stubbed) windows called Matador windows. (I will upload photos for all these soon).

Also, one can say that spanish villas have stairs from inside the houses, and a patio set on ground level, slightly elevated, which leads to the staircase. Ceilings are also of varied heights in spanish villas.

Overall, french villas used the purity of colors whereas, spanish villas showed the moslem influences they got over centuries.