MYTS 2019 — Grade 4 — Round 1

An writes the letters $M,Y,T,S$ repeatedly, obtaining the sequence

$MYTSMYTSMYTSMYTS\ldots$

What is the 2019th letter from the left?

The figure consists of six small squares. How many paths from $A$ to $C$, along the edges of the squares, avoid $B$ and have length five times the side length of a small square?

After a piece is removed from Minh’s Rubik’s cube, the following part remains:



Which of the following is the removed piece?

How many rectangles in the figure have length twice their width?

Lâm has 20 blue marbles and Vỹ has 19 red marbles. Lâm exchanges his blue marbles for Vỹ’s red marbles at a rate of 2 blue marbles for 1 red marble. After several exchanges, Lâm has 15 marbles in total. How many red marbles does Vỹ then have?

Hà has four stickers numbered 1, 2, 3 and 4 as shown below.



Hà places sticker 3 on sticker 4, then sticker 2 on sticker 3, and finally sticker 1 on sticker 2, aligning the squares marked $X$ and $Y$ on all four stickers exactly. Which of the following figures is obtained?

An airplane makes consecutive flights between Hà Nội and Hồ Chí Minh City, alternating directions. Each flight takes 2 hours 15 minutes, and the break between consecutive flights is 45 minutes. If the first takeoff from Hà Nội is at 5:30 a.m., how many times has the airplane taken off by 11 p.m. that day?

Find $A-B$, where

$$A=\frac{3}{1\times2}+\frac{7}{3\times4}+\frac{11}{5\times6}+\frac{15}{7\times8},\qquad B=\frac{5}{2\times3}+\frac{9}{4\times5}+\frac{13}{6\times7}.$$

At 8:05 a.m. a digital clock displays 08:05, and at 9:09 p.m. it displays 21:09. From noon today to noon tomorrow, how many times does the clock display all four digits 2, 0, 1 and 9?

For Tết, each of Minh, Lan, Phương and Hồng buys either a peach tree or a mai tree. Together they buy one pale-pink peach tree, one deep-pink peach tree, one yellow mai tree and one white mai tree. Given that:

- Minh and Lan buy different types of tree (peach or mai).
- Hồng does not buy a mai tree.
- Phương does not buy the yellow mai tree.

Which tree does Phương buy?

This year, Châu’s weekly swimming lessons are on Wednesdays from 2:00 to 3:00 and on Sundays from 2:00 to 3:30. According to this schedule, how many minutes of swimming lessons does Châu have in March? 8 March falls on a Friday.

Using the four digits 0, 1, 2 and 9, how many numbers less than 2019 and divisible by 3 can be formed, with each digit occurring at most once in any number?

For a school trip, a school can rent 24-seat and 36-seat buses. A 24-seat bus costs 3 million đồng, and a 36-seat bus costs 5 million đồng. What is the least cost of renting enough buses for 100 pupils? Give the answer in millions of đồng.

Thái has eight fence panels of length 2 metres and two of length 3 metres. What is the greatest area of a rectangular plot that Thái can enclose using these panels? (The fences form the sides of the plot; panels may not be cut or bent.) Give the answer in square metres.

The subtraction $\overline{MYTS}-\overline{HTH}$ gives a two-digit number. What is the smallest possible value of that number? The letters $M,Y,T,S,H$ represent distinct digits.