IKMC 2010 - Grades 3-4 - Self-study

There is a maze in the picture for a cat and a mouse. The cat can reach the bowl with milk, the mouse can reach the cheese, but the cat and mouse will never meet. What does the hidden part of the maze look like?

A 40-minute lesson started at 11:50. Exactly in the middle of the lesson, a bird suddenly flew into the classroom. When did that happen?

An Indian chief has three feathers, an axe, arrows and moccasins on his feet. His son has two feathers and arrows, has no axe, is barefooted and has two stripes drawn on his chest. Which picture shows the chief together with his son?

In this restaurant, a first course costs €4, a main course €9 and a dessert €5. The Menu, consisting of all three courses, costs €15. How much does someone save by ordering the Menu instead of the three separate courses?

Six coins are lying in a triangle. Move some coins to place them in a circle as in the second picture. What is the least number of coins that must be moved?

Four friends were eating ice cream. Maria ate more than Faria. Jaweria ate more than Veena. Jaweria ate less than Faria. Which list orders the girls from the one who ate the most to the one who ate the least?

Using only tiles like the one shown, which of the following patterns is impossible to construct when covering the floor of a room?

Centipede Eve has 100 feet. Yesterday she bought and put on 16 pairs of new shoes. Even then, 14 of her feet were still bare. On how many feet did she have shoes before shopping?

Mary folded and unfolded a paper four times along the lines indicated. How many of these folds made the kangaroos overlap exactly?

Mansoor and Sara live in a skyscraper. Sara lives 12 floors above Mansoor. One day Mansoor went upstairs to visit Sara. Halfway along his journey he was on the 8th floor. On which floor does Sara live?

A larger cube is made from 64 equal-sized little white wooden cubes. Five faces of the larger cube are colored green. How many little cubes have three green faces?

A ferry can take either 10 small cars or 6 lorries across the river at a time. On Wednesday it crossed the river five times, always full, transporting 42 vehicles. How many small cars did it transport?

A square is divided into four equal smaller squares, each colored green or blue. The four colorings shown count as the same coloring. How many different colorings are possible?

Jamil starts a chain letter by sending it to Pervaiz. Pervaiz sends it to two other people. Everyone who receives it also sends it to two other people. After two rounds a total of $1+2+4=7$ people have received it. How many people in total have received it after four rounds?

Children measured the same length of a sand playground by walking equal steps. Ali took 15 steps, Bisma 17, Dani 12 and Zoha 14. Whose steps were the longest?

The product $60\times60\times24\times7$ equals:

Two years ago, the sum of the ages of the cats Tony and Tiny was 15 years. Tony is now 13 years old. In how many years will Tiny be 9 years old?

Camilla wrote all positive integers from 1 to 100 in order in a chart with five columns. Part of the chart is shown. Her brother cut out part of the chart and erased some numbers. Which picture can represent the incomplete chart?

Some segments are numbered 1, 2, …, 8 as shown. Annie cuts along four of them in order to fold the paper into the figure below. What is the sum of the numbers of the segments she cuts?

Each of Basit’s friends added the day number and the month number of their birthday and obtained 35. Their birthdays are all different. What is the maximum possible number of Basit’s friends?