MYTS 2019 - Grade 4 - Round 2

A box contains 10 yellow marbles and some blue and red marbles. It is known that:

(a) The blue and red marbles together make up $\frac34$ of all the marbles;

(b) There are 10 more red marbles than blue marbles.

How many blue marbles and how many red marbles are in the box? (Enter the blue count, then the red count, separated by a comma.)

Two paths, each 1 m wide, are paved across a square garden as shown below. They divide the garden into four rectangular plots. The combined area of the paths is 35 m². Find the total area of the four rectangular plots. (Enter the number of square metres.)

Each letter $M,Y,T,S,V,N$ represents a digit less than 6, and different letters represent different digits. The numbers $\overline{MYTSVN}$, $\overline{YTSVN}$, $\overline{TSVN}$, $\overline{SVN}$, $\overline{VN}$ are divisible by 5, 11, 9, 6, 8, respectively. What is $\overline{MYTSVN}$?

Đắc, Lan and Hương challenge you to guess a number. They give the following information.

Đắc says:
- It has one digit.
- It is divisible by 5.

Hương says:
- It has one digit.
- Its remainder when divided by 9 is 8.

Lan says:
- It has two digits.
- It is divisible by 3.
- It is divisible by 8.

To make the puzzle difficult, each friend deliberately makes exactly one false statement. What is the number? Explain why.

Lan and Điệp use matchsticks to build houses. Lan builds separate houses as in Figure 1, whereas Điệp builds one row of adjoining houses as in Figure 2.

Together they have built 20 houses using 108 matchsticks in total. How many houses did Lan build?