SEAMO 2026 Paper C SET 3 – Self-practice

A new operation is defined by $m*n=m^n$. Find $n$ in $n*5=243$.

Select 8 distinct numbers from 1 to 9 to fill each blank below. What is the greatest possible result? $$[\square\div\square\times(\square+\square)]-[\square\times\square+\square-\square].$$

A cube has 8 vertices as shown. How many triangles can be formed by connecting any 3 vertices?

In 2018, Lucas invested 1000 dollars for 2 years. By the end of the first year, his investment suffered an 18% loss. In the second year it gained 25% on the remaining amount. Over the two-year period, what was the percentage change in his investment?

$\triangle AED$ and $\triangle BFC$ are identical isosceles triangles. The area of $\triangle AED$ is 202 square centimetres. Find the area of rectangle ABCD.

Find the possible values of $m$ such that the 101-digit number below is divisible by 7. $$\underbrace{66\ldots6}_{50\text{ digits}}\,m\,\underbrace{55\ldots5}_{50\text{ digits}}.$$ Source language discrepancy: the Vietnamese wording says the 101st digit, rather than the 101-digit number.

In the 4 ×4 grid shown, each line segment measures 1 unit. What is the longest distance (in units) a beetle can travel from Point A to Point B if each line segment can only be traversed once?

How many triangles are there in the figure below?

How many ways are there to choose two different numbers from the set {5, 6, 7, 8,…, 15} such that their sum is even?

After Wattana spent 35 dollars on a wallet, he and James had money in the ratio 3:4. Wattana then received 220 dollars and James spent 50 dollars. Finally Wattana had twice as much as James. How much money did Wattana have at first?

If $A=2^{248}$ and $B=3^{155}$, then which statement holds?

Evaluate $$\frac{(1+7)(1+\frac72)(1+\frac73)\cdots(1+\frac79)}{(1+9)(1+\frac92)(1+\frac93)\cdots(1+\frac97)}.$$

Each letter represents a unique non-zero digit in the addition below. What is the minimum value of $H+I+J$? $$\begin{array}{rrr}A&B&C\\D&E&F\\\hline H&I&J\end{array}\qquad ABC+DEF=HIJ.$$

Cindy used 12 matchsticks to make a 2 ×2 grid, 24 matchsticks to make a 3 ×3 grid, and 1300 matchsticks to make an m ×m grid. What is m?

In the quadrant shown, which statements are correct? Take $\pi=22/7$. (i) $A=28$ square centimetres; (ii) $A=30$ square centimetres; (iii) $A=B$; (iv) $A>B$.

$\triangle ABC$ is equilateral. The shortest distances from point O to its sides are 4, 5, 6 units respectively. Find the height of $\triangle ABC$.

Find $11+22+33+\cdots+1089+1100$.

Find $\angle m$ in $\triangle ABC$. (The diagram is not drawn to scale.)

How many numbers from 1000 to 1999 have a ones digit greater than their hundreds digit?

A fair die is rolled twice. What is the probability that the sum of the two outcomes is prime?

Source language discrepancy: the Vietnamese source instead asks that both outcomes are prime.