IKMC 2008 - Grades 5-6 - Self-study

Which is the smallest?

By what can the kangaroo symbol be replaced to make the displayed equation true?

Javed likes to multiply by 3, Parvaiz likes to add 2, and Naveed likes to subtract 1. In what order should they perform their favorite actions to convert 3 into 14?

To make the equality $1+1\clubsuit1-2=100$ correct, we should replace $\clubsuit$ with:

Numbers 2, 3, 4 and one more number are written in the cells of a 2 × 2 table. The first row sums to 9 and the second row sums to 6. The unknown number is:

Before the snowball fight, Ali had prepared a few snowballs. During the fight, he made another 17 and threw 21 at the other boys. Afterwards he had 15 left. How many had he prepared before the fight?

The first picture is a small piece of a multiplication table. The second is another one with some missing numbers. What is the number in the square with the question mark?

In a toy shop a four-floor black and white “brickflower” is displayed (picture 1). Each floor is made of bricks of the same colour. Picture 2 is its top view. How many white bricks were used?

Source colour note: the printed text says black and white, but the original coloured figure uses green and white; those original colours are preserved.

With what number of identical matches is it impossible to form a triangle? The matches should not be broken.

There are 5 boxes, each containing cards labeled A, B, O, R, V as shown. Peter removes cards so that each box ends with only one card and all five remaining letters differ. What card remains in box 5?

The triangle and square have the same perimeter. What is the perimeter of the whole figure, a pentagon?

A circular table is surrounded by 60 chairs. Some n people sit so that each is a neighbour of exactly one person. What is the largest possible value of n?

Here neighbours means people occupying immediately adjacent chairs.

By shooting two arrows at the aiming board shown, how many different total scores can we obtain? Missing the board is possible.

Rabia put her CDs into three cases, seven CDs in each. Two more CDs did not fit and stayed on the table. How many CDs does she have?

Which of the “buildings” (A), …, (E), each consisting of exactly 5 cubes, can you not obtain from the building on the right if you are allowed to move exactly one cube?

Source note: the stem says A–E, but only A–D are printed in this paper. All four actual choices are retained. Whole-building viewing rotations are allowed; cubes are not turned into a different shape.

Points A, B, C and D lie on a straight line in some order. AB = 13, BC = 11, CD = 14 and DA = 12. What is the distance between the farthest two points?

One face of a cube is cut along its diagonals as shown. Which of the following nets are impossible?

Seven cards numbered 1 to 7 lie in a box. The first person randomly takes 3 cards, the second takes 2, and 2 remain. The first says: “I know that the sum of your card numbers is even.” What is the sum of the first person’s cards?

For each two-digit number from 30 to 50, the units digit is subtracted from the tens digit. What is the sum of all the results?

At most how many digits can be erased from the 1000-digit number 20082008…2008 so that the remaining digits have sum 2008?