IKMC 2011 - Grades 5-6 - Self-study

Basil wants to paint the word KANGAROO. He paints one letter each day. He starts on Wednesday. On what day will he paint the last letter?

A motorcyclist rode a distance of 28 km in 30 minutes at a constant speed. At what speed did he drive, in km per hour?

A square of paper is cut into two pieces using a single straight cut. Which of the following cannot be the shape of either piece?

Hamster Fridolin sets out for the Land of Milk and Honey. His way to the legendary Land passes through a system of tunnels. There are 16 pumpkin seeds spread through the tunnels, as shown in the picture. What is the highest number of pumpkin seeds Fridolin can collect if he is not allowed to visit any junction more than once?

In Crazytown, all the houses on the right side of Number Street have odd numbers. However, Crazytowners don't use numbers containing the digit 3, though they use every other number. The first house on the right side of the street is numbered 1, and the houses are numbered in increasing order. What is the number of the fifteenth house on the right side of the street?

The picture shows a partially built cuboid. Which of the following pieces will complete the cuboid?

We pour 1000 litres of water into the top of the pipework shown in the picture. Every time a pipe forks, the water splits into two equal parts. How many litres of water will reach container Y?

The date 01-03-05 (1 March 2005) consists of three consecutive odd numbers in increasing order. This is the first date with this feature in the 21st century. Including 01-03-05, how many dates in the 21st century, when expressed in the form dd-mm-yy, have this feature?

The picture shows four cardboard pieces. All four pieces are put together without gaps or overlaps to form various shapes. Which of the following shapes cannot be made in this way?

When Liza the cat just lazes around, she drinks 60 ml of milk per day. But each day that she catches mice, she drinks a third more milk. In the last two weeks she has been catching mice every other day. How much milk did she drink in the last two weeks?

Andrew wrote the letters of the word KANGAROO in cells. He can write the first letter in any cell he wants. He writes every subsequent letter in a cell that has at least one point in common with the cell in which the previous letter was written. Which of the tables can Andrew not create in this way?

All 4-digit integers with the same digits as the number 2011 are listed in increasing order (so each number in the list has two 1s, one 0 and one 2). What is the difference between the two numbers appearing on either side of 2011 in this list?

Four of the numbers on the left are moved into the cells on the right so that the addition is correct. Which number remains on the left?

Nina used 36 identical cubes to build a fence of cubes around a square region. Part of her fence is shown in the picture. How many more cubes will Nina need in order to fill the region inside her fence?

Some square floors have been covered with white and grey tiles. Floors using 4 and 9 grey tiles are shown in the picture. Each floor has a grey tile in every corner and all the tiles around a grey tile are white. How many white tiles are needed altogether for a floor using 25 grey tiles?

Paul wanted to multiply an integer by 301, but he forgot the zero and multiplied by 31 instead. The result he got was 372. (He did manage to multiply by 31 correctly!) What result was he supposed to get?

In three games FC Barcelona scored three goals and let one goal in. In these three games, the club won one game, drew one game and lost one game. What was the score in the game FC Barcelona won?

We are given three points on a sheet of paper. The points are the vertices of a triangle. We want to draw another point so that the four points are the vertices of a parallelogram. How many possibilities are there for the fourth point?

The picture shows eight marked points connected by lines. One of the numbers 1, 2, 3 or 4 is to be written at each of the marked points so that the two numbers at the ends of every line are different. Three numbers have already been written. How many times does 4 appear in the completed picture?

Using only pieces like the one in the picture, Daniel wants to make a complete square without gaps or overlaps. What is the smallest number of pieces he can use?