MYTS 2017 - Grade 6 - Round 2

A forest contains 6 red, 3 blue, and 11 yellow chameleons. Whenever two differently coloured chameleons meet, both change to the third colour. Can all 20 chameleons become the same colour? Why?

Cut the shape with the bold boundary into three congruent shapes, cutting only along the square grid lines. Two shapes are congruent if one can be placed exactly over the other.

The diagram is a pyramid of 21 squares. Fill each square with a natural number so that every entry above the bottom row is the sum of the two entries immediately below it. The filled diagram gives an example. Mr Thuận wants exactly seven even entries. Show one such filling.

How many two-digit positive integers have a digit sum divisible by 3 but not by 2?

In triangle ABC, D and E lie on BC with BD = DE = EC, and F lies on AC with AF = FC. In the diagram G is the intersection of AD and BF, and J is the intersection of AE and BF. Given that the area of ABC is 480 cm², find the areas of (a) triangle BGD; (b) triangle AGJ.

N students stand in a circle numbered 1,2,…,N clockwise. Student 1 stays, student 2 leaves, the next stays, the next leaves, and so on, continuing around the shrinking circle until only one remains. Which numbered student survives when (a) N=32; (b) N=2017?