VTMO 2021 — Grade 3 — titan-cup

Find $B - A$, where $A=1+4+7+10+13+16+19+22+25+28+31$ and $B=2+5+8+11+14+17+20+23+26+29+32$.

A mother has five identical cards. In how many ways can she distribute all of them to two brothers, allowing one brother to receive none?

Nhi receives $1285000$ dong for Tet. What is the least number of banknotes, given that exactly one is a $500000$-dong note?

Bao and Hai have $51$ marbles. Bao gives Hai five, but Hai loses three. Their counts then become equal. How many did Hai originally have?

A rapid math contest has ten questions. A correct answer earns $4$ points; a wrong or blank answer loses $1$. What is the least number Thanh must answer correctly to score more than $20$?

Gray square cards form the pattern below. How many are needed for figure $100$?

Dao and Hang begin with equal candy counts. Each day Dao eats three and Hang two. Later Dao has five and Hang thirteen. How many did each start with?

Different letters $V , T , M , O$ represent different digits in $\overline{OM}\times T=\overline{V8}$. Find the least possible $V+T+M+O$.

Given $V , T , M , O , O , V , T , M , M , O , V , T , M , O , V , T , M , O , \ldots$, what is the $202$ nd character?

Jerry pairs the numbers $1$ through $25$ so that one number divides the other in every pair, such as $\left(1 , 7\right) , \left(5 , 15\right)$. What is the least number left unpaired?

An travels $S$ → A $_{1}$ → A $_{2}$ → $F$ and Binh $S$ → $B _{1}$ → $B _{2}$ → $F$. An’s route is $10 m$ longer. How much longer is A $_{2} F$ than $B _{2} F$?

A bag of candies divides equally among eight pupils. Four more join, so each receives two fewer than planned. How many candies are there?

Two squares of side $10 \,\mathrm{cm}$ form the figure. Find the unshaded area minus the shaded area.

Place $1$ through $8$ once each in the small circles so that each large circle’s entries sum to $22$. What is the greatest possible product of the two question-mark entries?

Duc’s marbles are numbered $1 , 3 , 5 , 7 , 9$ and Hai’s $0 , 2 , 4 , 6 , 8$. Nhi takes one from each and adds them. How many distinct sums are possible?

The Fibonacci sequence is $1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , \ldots$ How many of its first hundred terms are odd?

In the example tower, each cell sums the two below. Arrange $1$ through $6$ in the bottom row to maximize the top cell. What is the maximum?

Fill the $3 \times 3$ table with equal row, column and diagonal sums. Find $A\times B\times C\times D\times E\times F$.

Fill in the question mark in the figure.

In this $4 \times 4$ Ken Ken, bold borders define cages labeled with a target and operation. For example, $7$+ means sum $7$; $2$− difference $2$; $2 \div$ quotient $2$; $4 \times$ product $4$. Fill each row and column with $1 \text{--} 4$ once each and satisfy every cage. What number is in the ★ cell?