IKMC 2013 - Grades 5-6 - Self-study

We put 2, 0, 1, 3 into an adding machine, as shown. What is the result in the box with the question mark?

Nathalie wanted to build the same cube as Diana had (picture 1). However, Nathalie ran out of small cubes and built only the part of the cube, as you can see in picture 2. How many small cubes must be added to fig. 2 to form fig. 1?

Find the distance which Mara covers to get to her friend Bunica.

Nick is learning to drive. He knows how to turn right but cannot turn left. What is the smallest number of turns he must make in order to get from A to B, starting in the direction of the arrow?

The sum of the ages of Ann, Bob and Chris is 31 years. What will the sum of their ages be in three years time?

What digit must be placed in all three boxes $\square\square\cdot\square=176$, in order to make the multiplication work?

Michael has to take a pill every 15 minutes. He took the first pill at 11:05. What time did he take the fourth pill?

By drawing two circles, Mike obtained a figure, which consists of three regions (see picture). At most how many regions could he obtain by drawing two squares?

The number 36 has the property that it is divisible by the digit in the unit position, because 36 is divisible by 6. The number 38 does not have this property. How many numbers between 20 and 30 have this property?

Ann has a lot of pieces like the one in the picture. She tries to put as many as possible in the 4 by 5 rectangle. The pieces may not overlap each other. What is the largest possible number of pieces Ann can put in the rectangle?

Which of the following pieces covers the largest number of dots in the table?

Mary shades various shapes on square sheets of paper, as shown. How many of these shapes have the same perimeter as the sheet of paper itself?

Ann rides her bicycle throughout the afternoon with constant speed. She sees her watch at the beginning and at the end with the following result. Which picture shows the position of the minutes hand when Ann finishes one third of the ride?

Matthew is catching fish. If he had caught three times as many as he actually did, he would have 12 more. How many fish did he catch?

John has made a building of cubes. In the picture you see this building from above. In each cell you see the number of cubes in that particular tower. When you look from the front, what do you see?

In an election each of the five candidates got a different number of votes. The candidates received 36 votes in total. The winner got 12 votes. The candidate in last place got 4 votes. How many votes did the candidate in second place get?

From a wooden cube with side 3 cm we cut out at the corner a little cube with side 1 cm (see picture). What is the number of faces of the solid after cutting out such a small cube at each corner of the big cube?

Find the number of pairs of two-digit natural numbers whose difference is equal to 50.

The final of the local hockey championship was a match full of goals. There were 6 goals in the first half and the guest team was leading after the first half. After the home team scored 3 goals in the second half, they won the game. How many goals did the home team score altogether?

In the squares of the $4\times4$ board numbers are written such that the numbers in adjacent squares differ by 1. Numbers 3 and 9 appear in the table. Number 3 is in the top left corner as shown. How many different numbers appear in the table?