Thursday, 10 October 2013

colour problem

Ball and Colour problem: There are certain number of balls and they are painted with the following conditions:
  • Every two colours appear on exactly one ball.
  • Every two balls have exactly one colour in common.
  • There are four colours such that any three of them appear on one ball.
  • Each ball has three colours.
Find the number of balls and the number of colours used.

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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...