Mathematics Olympiad Round 1

Four cards lie in a row

{2} {0} {1} {7}

which row of cards can you not obtain if you can only swap two cards?

• {2} {7} {1} {0}

• {0} {1} {2} {7}

• {1} {0} {2} {7}

• {0} {2} {1} {7}

Mike cuts a pizza into quarters. Then he cuts every quarter into thirds. What part of the whole pizza is one piece?

• a third

• a quarter

• an eighth

• a twelfth

Kalle knows that 1111 * 1111 = 1234321. How much is 1111*2222?

• 3456543

• 2345432

• 2234322

• 2468642

While Peter is solving 2 problems in an exam, Nick manages to solve three problems. Totally the boys solved 30 problems. How many problems did Nick solve more than peter?

• 5

• 6

• 7

• 8

On a planet there are 10 islands and 12 bridges. All bridges are open for traffic right now. What is the smallest number of bridges that must be closed in order to stop the traffic between A and B.1

• 1

• 2

• 3

• 4

A thread of length 10cm is folded into equal parts as shown in the figure.

The thread is cut at the two marked places. What are the length of the three parts?

• 2cm, 3cm, 5cm

• 2cm, 2cm, 6cm

• 1cm, 4cm, 5cm

• 1cm, 3cm, 6cm

Alice's mother wants to see a knife on the right side of each plate and a fork on the left side. How many interchanges of a knife and a fork does Alice need to make in order to please her mother.

• 1

• 2

• 3

• 5

The number 4 is next to two mirrors so it reflects twice as shown. When the same thing happens to number 5, what do we get instead for the question mark?

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Which of the following figures cannot be formed by gluing these two identical squares of paper together?

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A big cube was built from 8 identical small cubes, some black ones, and some white ones. Five faces of the big cube are:

What does the sixth faces of the big cube look like?

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