In a Sudoku the numbers 1, 2, 3, 4 can occur only once in each column and once in each row. In the mathematical sudoku on the picture, Patrick first writes in the results of the calculations. Then he completes the sudoku. Which number will Patrick put in the grey cell ?

Grandmother made 20 gingerbread biscuits for her grandchildren. She decorated 15 biscuits with raisins and then 15 biscuits with nuts. At least how many biscuits were decorated both with raisins and nuts ?

Among Nikolay’s classmates there are twice as many girls as there are boys. Which of the following numbers may be equal to the number of all children in this class ?

In the animal’s school, three kittens, four ducklings, two goslings and several lambs are talking lessons. The teacher owl found out that all of her pupils have 44 legs altogether. How many lambs are among them ?

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 ?