MYTS 2017 - Grade 5 - Round 2

The diagram is a pyramid of 15 squares. Write a natural number in each square so that, except in the bottom row, each number is the sum of the two numbers immediately below it. The filled diagram gives an example. Mr Thuận wants a filling with exactly five even numbers. Show one such filling.

There is one card labelled 0, two labelled 1, one labelled 5, one labelled 7, and one labelled 8. How many six-digit natural numbers can be formed by placing all six cards in a row?

ABCD is a square. E, F, G and H are the midpoints of AB, AD, BC and CD respectively. The area of ABCD is 120 cm². Find the total shaded area, in square centimetres.

Mr Dư has four distinct coins, each bearing exactly one letter on each side. He can arrange these coins to form each of the words shown: HOI, TOAN, TIN, TAI, NANG. Determine the pairs of letters on the four coins.

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.

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?