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.

A cake weighs 900 g. Paul cuts it into 4 pieces. The weight of the largest piece is the same as the total weight of the other three pieces. What is the weihgt of the largest piece ?

Two big rings – one grey, one white – are linked to each other. Peter, in front of the rings, sees the rings as in the picture:

Paul is behind the rings. What does he see ?

In the following addition, some of the digits have been replaced by stars.

What is the sum of the missing digits ?

What is the difference between the smallest 5-digit number and the largest 4-digit number ?

A square of perimeter 48 cm is cut into 2 pieces to make a rectangle ( see the picture )

What is the perimeter of the rectangle ?

Katrin has 38 matches. She built a triangle and a square, using all the matches. Each side of the triangle consists of 6 matches. How many matches are in each side of the square ?

A Ferris wheel has 32 passenger cabins. If you are sittin in cabin 14 which ic currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel ?

The pearl necklace in the picture contains black pearls and white pearls.

Arno wants to have five of the black pearls. He can only take pearls from either end of the necklace, and so he has to take some of the white pearls also. What is the smallest number of white pearls Arno has to take ?

Harry participated in a broom flight contest which consisted of five laps. The times when Harry passed the starting point are shown in the table. Which lap took the shortest time ?

It takes Ben 30 minutes to cut a long log of wood into six pieces. How long does it take him to cut another log of wood into nine pieces ?

Which tile must be added to the picture so that the light grey area is as large as the black area ?

Henry and John started walking from the same point. Henry went 1 km north, 2 km west, 4 km south and finally 1 km west. John went 1 km east, 4 km south and 4 km west. Which of the following must be the final part of John’s walk so that he could reach the same point as Henry ?

The kangaroos A, B, C, D and E were sitting in this order, clockwise, around a circular table. When the bell rang, each kangaroo but one exchanged its position with a neighbour. The order of the kangaroos, clockwise, became A, E, B, D, C. Which kangaroo did not move ?

A square can be formed using four of these five pieces. Which one will not be used ?

A positive integer has three digits. The product of the digits is 135. What is the sum of the digits ?

In a restaurant, there are 16 tables, each with 3, 4 or 6 chairs. The tables with 3 or 4 chairs can accommodate 36 people. The restaurant can accommodate 72 people. How many tables are there with 3 chairs ?

The points A, B, C, D, E and F lie on a straight line in that order. We know that AF = 35, AC = 12, BD = 11, CE = 12 and DF = 16. What is the distance BE ?

Parisa sets her marbles in groups of equal size on the desk. After she arranged the marbles in groups of 3, she found that there were 2 marbles left. The she arranged the marbles in groups of 5, and again there were 2 marbles left. At least how many more marbles does she need so that there won’t be any left when she arranges them in groups of 3 and in groups of 5 ?