VTMO 2016 — Grade 3 — semifinal

Find $N$: $7\times6\times5\times9=30\times N$.

How should Pi order the three cards to form the greatest natural number? $P$ shows $08 , Q$ shows $5$, and $R$ shows $19$.

Minh has five stacks of books as shown. He must make all stacks equally high without changing the number of stacks. What is the fewest moves, if each move transfers one or two books?

The first rice bag contains $10 \,\mathrm{kg}$ more than the second. How many kilograms should be transferred from the first to the second to make them equal?

Given $x\otimes y=x\times y+x$, for example $4\otimes5=4\times5+4=24$, evaluate $3\otimes7$.

An and Binh collect badges. Even if Binh had five more, he would still have three fewer than An. How many fewer did Binh originally have?

Minh queues with his classmates for a trip. He is sixth from the front and tenth from the back. How many people are in the line?

How many squares are in the figure below?

Fill in the question mark in the figure.

Use each digit $1 , 2 , 3 , 4 , 5$ once, with $U , V , W , X , Y$ all different. What is the least value of $\overline{UVW}-\overline{XY}$?

A box contains five marbles numbered $1 , 4 , 7 , 10$ and $13$. Dung draws two without looking. How many distinct sums of the two numbers are possible?

Place digits $1$ through $6$ in the six circles so that side A sums to $13$, side $B$ to $13$, and side $C$ to $6$. What belongs in the top circle?

Numbers such as $112$ and $301$ have three digits summing to $4$. How many three-digit numbers have digit sum $4$?

An has twice as many candies as Binh. Binh has three times as many as Chau. Chau has four times as many as Dung. If Dung has five candies, how many do the four have altogether?

An has three boxes of pencils. He transfers $6$ from box $1$ to box $2$, then $4$ from box $2$ to box $3$, then $2$ from box $3$ to box $1$. Each box now contains $10$ pencils. How many were originally in box $2$?