(Solved):   28. A swimming medley consists of 100 metres of each of butterfly, backstroke, breaststrok ...

 

28. A swimming medley consists of 100 metres of each of butterfly, backstroke, breaststroke and freestyle, in that order. I swim freestyle 3 times faster than breaststroke, and butterfly twice as fast as breaststroke, and my backstroke is half as fast as my freestyle. It takes me 6 minutes to swim the full medley. To the nearest metre, how far will I have swum after 4 minutes? 29. An ant's walk starts at the apex of a regular octahedron as shown. It walks along five edges, never retracing its path. It visits each of the other five vertices exactly once. In how many different ways can the ant do this? 30. Consider a \( 15 \times 15 \) grict of umit squares, In the square in row \( a \) and column \( b \), we write the number \( a \times b \). We then colour the squares black and white in-a checkerboard fashion, so that the square labelled 225 is coloured white. The diagram shows the parts of the grid near each corner. What are the last three digits of the sum of the numbers in the white squares?