In one kangaroo family, there is a custom to name their babies by names, which consist of two letters of the word KANGAROO: the first letter is a consonant, the second letter is a vowel. How many different baby names can be composed ?

At a Christmas party, there was exactly one candlestick on each of the 15 tables. There were six five – branched candlesticks, and the rest were three-brandched ones. How many candles had to be bought for all the candlesticks ?

The figure consists of an equilateral triangle, a square and a regular pentagon. It is built by sticks of equal length. At most many such figures can be built with a box of 2012 sticks of equal length ?

Gregor forms two numbers with the digits 1, 2, 3, 4, 5 and 6. Both numbers have three digits, and each digit is used only once. Gregor adds these two numbers. What is the greatest sum Gregor can obtain ?

Laura, Iggy, Val and Kate want to be in one photo together. Kate and Laura are best friends and they want to stand next to each other. Iggy wants to stand next to Laura because he likes her. In how many possible ways can they arrange for the photo ?

A grasshoper wants to climb a staircase with many steps. She can make only two kinds of jumps: three steps up, or four steps down. Beginning at the ground level, at least how many jumps will she have to make in order to take a rest on the 22th step ?

Frank made a domino snake of seven tiles. He put the tiles next to each other so that the sides with the same number of dots touched. Originally the snake had 33 dots on its back. However, Frank’s brother George took away two tiles from the snake ( see the picture )

How many dots were in the place with the question mark ?

A special clock has three hands of different length ( for hours, for minutes, and for seconds ). We do not know which hand is which, but we do know that the clock runs corretly. At 12:55:30 pm, the hands were in the position depicted on the right. How will this clock look like at 8:11:00 p.m ?

A rectangular paper sheet measures 192 x 84 mm. You cut the sheet along just one straight line to get two parts, one of which is a square. Then you do the same with the non-square part of the sheet, and so on. What is the length of the side of the smallest square you can get with this procedure ?

In a soccer game the winner gains three points, while the loser gains zero points. If the game is a draw, then the two teams gain one point each. A team has played 38 games and gained 80 points. Find the greatest possible number of games that the team lost.

Beatrice has a lot of pieces like the grey one in the picture. At least how many of these grey pieces will she need to make a grey square ?

Peter bought a carpet 36 dm wide and 60 dm long. The figure shows part of this carpet. As seen, the carpet has a pattern of small squares containing either a sun or a moon. You can count that along the width there are nine squares. When the carpet is fully unrolled, how many moons will be seen ?

Nancy bought 17 cones of ice-cream for her three children. Misha ate twice as many cones as Ana. Dan ate more ice-cream than Ana but less than Misha. How many cones of ice-cream did Dan eat ?

Cristi has to sell 10 glass bells that vary in price: 1 euro, 2 euro, 3 euro, 4 euro, 5 euro, 6 euro, 7 euro, 8 euro, 9 euro, 10 euro. In how many ways can Cristi divide all the glass bells in three packages so that all the packages have the same price ?

Basil has several domino tiles, as shown in the figure. He wants to arrange them in a line according to the well-known “domino rule”: in any two tiles that are next to each other, the squares that touch must have  the same number of points. What is the largest number of tiles he can arrange in this way ?