4. 

The first child leaves the fourth point uncolored with green.

The second child leaves every fifth point uncolored with blue.

The third child leaves every sixth point uncolored with brown. $1 p$

The points that remain uncolored are multiples of 4, 5, and 6 respectively

LCM $[4,5,6]=60$

Finalize 3 points

$2 p$

Note: Any other correct solution is also scored.
4. Consider 300 collinear points. Three children color these points as follows. The first child colors the first three points green, then skips one, then colors the next three, and skips one again, and so on until the end of the 300 points. The second child performs a similar recoloring from the beginning, but with blue, coloring the first four points, then skipping one, and then the next four, and skipping one again, and so on. The third child recolors with brown, coloring five points at a time and skipping one, and then the next five, and so on. How many points remain uncolored at the end?

SGM 2014

## NOTE

- All questions are mandatory;
- Each question is worth 7 points;
- No points are awarded by default;
- The actual working time is 2 hours from the moment the questions are received.

Mathematics Olympiad

Local stage - February 20, 2015

## Grade 6