MYTS 2016 - Grade 6 - Round 1

On 15/03/2016, Thuan notices that the sum of the first four digits equals the sum of the last four digits. What is the last date in that year with this property? Write it in the same format.

Duong has 169 coins and wants to give some to each friend, with no two friends receiving the same number. What is the greatest possible number of friends?

Three semicircles are tangent at one point with diameters on one line and radii in ratio 1:2:4, as shown. The largest semicircle has area 160 cm². Find the shaded area in cm².

A class has 25 members;18 like pizza and 12 like spaghetti. What is the largest number who like neither food?

Calculate $(1+\frac 23)(1+\frac 24)(1+\frac 25)\cdots(1+\frac 2{97})(1+\frac 2{98})$.

N is a five-digit multiple of 11 containing exactly three distinct digits. What is the largest N?

The Olympic flag shows five circles intersecting at eight points. If the circles are moved so no two coincide, what is the maximum number of intersection points?

Three lines have at most three intersection points. If k lines have a maximum of 15 intersection points, find k.

A bag contains 5 green apples,8 yellow apples,10 green pears and 3 yellow pears. Nhi draws fruits one at a time without looking. How many must she draw to guarantee an apple and a pear of the same color?

The diagram shows 24 pigeons, one per occupied cell. What is the minimum number of pigeons that must move to other empty cells, not necessarily neighboring ones, so every row and every column contains the same number?

N contains each digit 0,1,...,9 exactly once and is divisible by 40. What is the largest N?

Positive odd integers fill the table shown, leaving one blank cell after every three filled cells. Which column contains 579?

Seven congruent rectangles form the larger rectangle ABCD as shown. If ABCD has area 756 cm², find its perimeter in centimeters.

The number 12 has six divisors 1,2,3,4,6,12. What is the smallest positive integer N having exactly 16 divisors, including 1 and itself?

A bag contains 25 marbles in three colors: blue, red, yellow. Drawing 21 without looking is necessary to guarantee all three colors. What is the greatest possible number of yellow marbles?

Cut the figure along the grid lines into two congruent pieces. Sum the numbers on each piece. What is the larger sum?

Today is Sunday, and in three days it will be Wednesday. Exactly 259 days from today is 11 December 2016, described in the source as South Africa’s national day (independence from Britain in 1931). What day of the week is it? The figure shows calendars for March and April 2016.

A natural number N is generous if divisible by every digit and by the digit sum. For example 12 is generous, but 102 is not. Find the smallest generous number divisible by 11.

In a chess tournament, each player plays every other player exactly once. There are 300 games. How many players participate?

A 2 × 3 × 4 cuboid K is built from unit cubes and has surface area 52 square units. If one unit cube is removed, what is the smallest possible surface area of the remaining solid?