VTMO 2026 - Grade 3 - Final - SET 2 - Self-study

On a Grade 3 outing, all the pupils stand equally spaced in a circle and number themselves clockwise. Minh is number 6 and stands directly opposite pupil number 14. How many pupils are on the outing?

How many natural numbers have pairwise different digits whose product is 12? Examples include 34 and 216.

Both scales below are balanced. Which statement is correct? A filled circle, square and triangle represent the weights of the corresponding objects.

Grey square tiles form the pattern shown. The first five figures are arranged from left to right. How many tiles are needed for figure 100?

Use all five pieces shown to make the $4×4$ square below. You may rotate pieces but may not turn them over. The grey cells hide their symbols. Which symbols are in the cells marked A and B?

Last Tết, Nhi received 1,285,000 đồng in lucky money. What is the fewest banknotes she could have received, given that exactly one was a 500,000-đồng note?

Evaluate $(23+24+25+26+27+28+29)-(13+14+15+16+17+18+19)$.

The operation $\circledast$ is illustrated by $\circledast 5=5+4+3+2+1$. Find $\circledast 10$.

Thanh has tiles made of four unit squares, in the shape shown. Which of the following figures can he make using some of these tiles, without gaps or overlaps?

Châu spends 40 thousand đồng on a book, then spends half of the money left on notebooks. After buying a pen for 12 thousand đồng, Châu has 13 thousand đồng left. How many thousand đồng did Châu have at first?

Minh has 30 ballpoint pens and markers altogether, in blue and red. There are 20 blue pens or markers, and 6 red markers. How many red ballpoint pens does Minh have?

An has three clocks, A, B and C. Over each common elapsed-hour interval, A gains 30 seconds relative to B, while B loses 30 seconds relative to C. At 8 a.m. all three are reset to 8 a.m. When C shows noon, what time does A show? Give hours, minutes and seconds.

Long and some friends sit around a circular table with a bag of 222 sweets. Long takes the first sweet and passes the bag to the person on his left. Each person then takes one sweet and passes the bag to the left. This repeats until Long takes the last sweet. What is the smallest possible number of people at the table?

An, Bình and Châu have some sweets. First, An gives Bình and Châu as many sweets as each already has: for example, if Bình has 10 and Châu has 7, An gives them 10 and 7 respectively. Next, Bình gives Châu and An as many sweets as each then has. Finally, Châu gives An and Bình as many sweets as each then has. After the third turn, each has 16 sweets. How many sweets did An have at first?

Khôi has seven coloured pencils in a box: red, orange, yellow, green, blue, indigo and violet. Each time, Khôi takes out a pencil, writes its Vietnamese colour word, then puts it back. The words are ĐỎ, CAM, VÀNG, LỤC, LAM, CHÀM and TÍM. For example, taking red means writing “ĐỎ”, which has 2 letters. Accent marks do not count as extra letters.

Every pencil is taken out at least once. The seven numbers of times they are taken out are all different. The violet pencil is taken out 9 times, more than any other. What is the greatest total number of letters Khôi could write?

A kind of flower lasts six days: it is white on days 1,2,3; pink on days 4,5; and yellow on day 6, then it withers. The observed counts are shown below. Yesterday there were 5 white,4 pink,3 yellow flowers; today there are 7 white,6 pink,0 yellow flowers. If two new white flowers bloom tomorrow and there are exactly four pink flowers tomorrow, how many white flowers will there be tomorrow?

A notebook costs 8,000 đồng and a pen costs 5,000 đồng. Pi buys 5 notebooks and 6 pens and has 20,000 đồng left. How much money did Pi have at first? Show your working.

The product of 13 natural numbers is 13. What is their sum?

A division has divisor 9, quotient 11 and remainder 8. How much must be added to the dividend to make the division exact and increase the quotient by 2?

Peter rabbit starts at the position shown and wants to get home as quickly as possible by moving only up or right. He collects the number of carrots shown in each square he visits. What is the greatest number of carrots he can collect?
In the diagram, “Nhà” means “Home”.