MYTS 2017 - Grade 6 - Round 1

Two small squares of areas 4 cm² and 9 cm² lie inside a square of area 81 cm² as shown. Find the coloured area in cm².

Find the smallest three-digit natural number N whose digit sum is 13.

A kingdom has fat monsters with 3 heads and 6 arms, and thin monsters with 1 head and 10 arms. A warrior counts 10 monsters with 16 heads. How many arms are there in total?

Find the smallest natural number N divisible by 33, with all digits odd and pairwise distinct.

The rectangle is cut into 16 congruent right trapezoids as shown. Each trapezoid’s shorter base is 3 cm. Find the rectangle’s area in cm².

Find the smallest seven-digit natural number with distinct digits, divisible by 7, whose digit sum is also divisible by 7.

Identical polygonal paper pieces shaped like lizards are fitted together as shown. Each lizard must have one colour and neighbouring lizards must have different colours. What is the least number of colours needed?

How many four-digit numbers have digit sum 4?

151 is a palindrome because reversing its digits gives the same number. How many three-digit palindromes are there?

BEAUTIFUL is repeated in a row until there are exactly 500 letters. What are the last two letters, in order?

Find the smallest three-digit natural number N divisible by 77 whose digits are all odd.

ABCD is a trapezoid of area 198 cm². Quadrilaterals EKHL and GMJN have areas 32 cm² and 41 cm². Find the total coloured area in cm².

Find the largest six-digit multiple of 15 whose digits are all distinct.

Houses are numbered with consecutive odd numbers 1,3,…,29. Cutting each metal digit costs 30000 đồng. What is the total cost, in đồng?

The C-shaped solid is built from identical cubes of side 2 cm as shown. Find its total surface area in cm².

Dân, Chủ, Văn, Minh and Việt line up for a photograph. How many orders have Dân next to Việt?

Join each vertex of a square to the midpoint of the opposite side as shown. The square’s area is 200 cm². Find the coloured area in cm².

In a class,3/5 of the girls and 1/2 of the boys wear glasses. Equal numbers of girls and boys wear glasses. Find the fraction of the class not wearing glasses.

How many triangles are in the diagram?

Fill in a number you consider suitable:2,5,11,20,35,59,98,?.