IKMC 2011 - Grades 9-10 - Self-study

A zebra crossing has alternating white and black stripes, each 50 cm wide. It starts and ends white, and has 8 white stripes. What is the total width?

The shaded rectangle has area 13 cm². X, Y are the midpoints of the trapezium’s sides. Find the trapezium’s area.

Let $P=2\times3+3\times4+4\times5$, $Q=2^2+3^2+4^2$, $R=1\times2+2\times3+3\times4$. Which statement is true?

Write a number at every lattice dot so the sum at the ends of each segment is the same. Two numbers are given. What is x?

Dividing 2011 by a number gave remainder 1011. Which of 100,500,1000 was the divisor?

A rectangular mosaic of area 360 cm² uses equal square tiles. It is 24 cm high and 5 tiles wide. Find one tile’s area.

All four-digit numbers whose digits sum to 4 are listed in descending order. What position is 2011?

Each shown segment is a rotation of the other. Which marked points can be rotation centres?

The shape consists of a regular hexagon of side 1, six triangles and six squares. Find its perimeter.

Three normal dice are stacked so touching faces always sum to 5. A visible face of the bottom die has one pip. What is on top of the top die?

A month had 5 Mondays,5 Tuesdays,5 Wednesdays. The preceding month had only 4 Sundays. What must the next month include?

After a race started, Michael led Fernando then Sebastian. Michael/Fernando exchanged places 9 times, Fernando/Sebastian 10 times, Michael/Sebastian 11 times. Find their finishing order.

Given $9^n+9^n+9^n=3^{2011}$, find n.

Cubes have sides a dm and (a+1) dm. The larger is full, the smaller empty. Pouring enough water to fill the smaller leaves 217 litres in the larger. How many litres were poured?

A marble of radius 15 just fits the conical hole as shown. The axial side-view section is equilateral. How deep is the hole?

Colour each 4 × 4 cell black or red. Row/column labels give required black counts. How many colourings are possible?

What is the longest run of consecutive three-digit numbers, each containing at least one odd digit?

Fill integers into the 3 × 3 grid so every 2 × 2 square sums to 10. Five entries are given. Find the sum of the four missing entries.

Jane sketched four streets, their seven crossings and friends’ houses during a rough sailing trip. In reality Arrow, Nail and Ruler Streets are straight; the fourth is Curvy Road. Who lives on Curvy Road?

Choose Z on XY in triangle WXY, and T on WZ as shown. What is the least possible number of distinct values of the nine marked angles?