VTMO 2026 - Grade 3 - Final - SET 5 - Self-study

Find the missing term: $1,1,2,6,\square,120$.

The numbers 1,2,3,4,5,6,7,8,9 are placed in the nine squares, each once. The vertical total and horizontal total both equal 23. What number is in the middle?

Nam has the five pieces shown. Which shape below cannot be made using all five pieces without overlap?

Mother has five identical cards. In how many ways can she distribute all of them between two siblings? Either sibling may receive none.

The numbers are placed in the tower according to a rule. Calculate $A+B$.

A playing piece starts at A on a circular board. On move 1 it advances one space from A to B; on move 2 it advances two spaces from B to C; on move 3 it advances three spaces from C to D; and so on. After 15 moves, it has travelled exactly one full circuit and returns to A. How many spaces are on the board?

How many seven-digit numbers $\overline{A623B4C}$ make both $\overline{47A1B25}$ and $\overline{A623B4C}$ divisible by 3? A, B and C are digits.
Examples:
• 2623341 qualifies because 4721325 and 2623341 are both divisible by 3.
• 4623145 does not qualify: 4741125 is divisible by 3, but 4623145 is not.

Bảo and Hải have 51 marbles altogether. Bảo gives Hải 5 marbles, but Hải loses 3 marbles. They then have equal numbers of marbles. How many did Hải have at first?

The difference between two three-digit numbers is 217. What is the greatest possible sum of the two numbers?

The large cube shown is made from 8 small cubes. How many faces of the small cubes touch another small cube?

Three books, Literature, Mathematics and Science, lie on a table. Their covers are blue, red and yellow, one of each colour. The red book lies between the Literature and Science books. The Science book and the blue book were bought on the same day. What colour is the cover of each book? Give the colours in this order: Literature, Mathematics, Science.

Sơn buys 3 notebooks and 5 pencils for 81,000 đồng. Bình buys 3 notebooks and 7 pencils for 105,000 đồng. How much does one notebook cost, and how much does one pencil cost? Show your reasoning.

If 1 pupil moves from class 3A to class 3B, the two classes have equal numbers of pupils. If 1 pupil moves from class 3B to class 3C instead, class 3C has 2 more pupils than class 3B. Which class originally had the most pupils?

Khang visits an amusement park with two payment options.
Option 1: 150,000 đồng admission, plus 30,000 đồng per game.
Option 2: 350,000 đồng for admission and unlimited games.
Khang chooses option 1 because it costs less than option 2. What is the greatest number of games he could have played?

A class has 10 pupils. The teacher has 80 sweets. She gives each girl the same number of sweets and has 3 left. There are more girls than boys. How many boys are in the class? Explain.

Find the sum of the two numbers in the 10th pair:
$(1,6);(3,8);(5,10);(7,12);\ldots$

An electronic display has 45 small LEDs, one for each small square. The display currently shows 621 as below. What is the fewest LEDs that must be switched on or off to show 208?



The patterns for digits 0 through 9, in order, are shown here:

How many triangles are in the figure?

Fifty cakes are packed into small boxes holding 4 cakes each and large boxes holding 6 cakes each. Fewer than 10 boxes are used, and every box is full. How many large boxes are used?

In a rectangular flower garden, the original wording says that there are 4 flowers at each of the four corners. Mai counts 30 flowers along the length and 20 along the width. The flowers are equally spaced, with 25 cm between consecutive flowers. What is the perimeter of the garden, in centimetres?
Clarification for this version: use the side labels 30 and 20 as the numbers of flower positions along one full side, including its endpoints. The wording about 4 flowers at each corner and the partial doubled row in the drawing are inconsistent; see the solution note.
The diagram label “hoa” means “flowers”.