VTMO 2021 — Grade 4 — cup

Dao and Hang initially have equal numbers of candies. Dao eats $6$ per day and Hang $4$. After some days Dao has $6$ left and Hang $14$. How many candies did each initially have?

An uses exactly $50$ matches to form digits in the illustrated style, then adds their values. What is the greatest possible sum?

Among birth years from $1900$ to $2021$, how many give an age equal to the digit sum of the birth year? Age $= 2021$−birth year.

A teacher has enough candies to divide equally among $8$ students. When $4$ more join, each receives $2$ fewer candies than planned. How many candies are there?

The Fibonacci sequence starts $1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , \ldots$ How many of the first $100$ terms are even?

Tom writes more than one consecutive two-digit odd number. Their sum is $161$. What is the middle number?

Five congruent small rectangles are placed in a $24 \,\mathrm{cm}$ by $18 \,\mathrm{cm}$ rectangle as shown. Find the area of a small rectangle.

Find ? in the diagram (circles, triangles and squares each have a fixed value; the number beneath a group is its sum).

An and Binh take equal-length routes from $S$ to $F$. An: $S$→A $_{1}$→A $_{2}$→A $_{3}$→A $_{4}$→A $_{5}$→A $_{6}$→A $_{7}$→A $_{8}$→A $_{9}$→$F$; Binh: $S$→$B _{1}$→$B _{2}$→$F$. $SB _{1} = 50 m$ and $SA _{1} = 30 m$; see the diagram. Find A $_{2}$ A $_{3}$+A $_{4}$ A $_{5}$+A $_{6}$ A $_{7}$ in metres.

Solve the illustrated $4 \times 4$ Ken Ken. Each row and column contains $1 , 2 , 3 , 4$. Each bold cage has an operation and target: $7$+ means sum $7 , 2$− difference $2 , 2 \div$ quotient $2$, and $4 \times$ product $4$. What is the starred cell?

A teacher writes two natural numbers. An says their product is odd; Binh says their quotient is $4$; Chau says their sum is divisible by $5$; Dung says their difference is $123$. Exactly three statements are true and one false. Find the numbers.

All $15$ students in $IQ = 4$ A receive candies. Seven get more than $1$, five more than $2$, three more than $3$, one gets $5$, and nobody gets more than $5$. How many candies are given in total?