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 ?

In December Tom-the-cat slept for exactly 3 weeks. Which calculations should we do  in order to find how many minutes he stayed awake drung this month ?

There are oranges, apricots and peaches in a big basket. How many fruits are there in the basket if the peaches and the apricots together are 18, the oranges and the apricots together are 28 and 30 fruits are not apricots ?

In the shown triangle, first we join the midpoints of all the three sides. This way, we form a smaller triangle. We repeat this one more time with the smaller triangle, forming a new even smaller triangle, which we colour in red. How many triangles of the size of the red triangle are needed to cover completely the original triangle, without overlapping ?

Note: Midpoint of a side is the point that divides the side in two parts of the same length.

Children in the school club had to arrange fitness balls according to their size from the biggest to the smallest one. Rebecca was comparing them and said: the red ball is smaller than the blue one, the yellow one is bigger than the green one, and the green one is bigger than the blue one. What is the correct order of the finess balls ?

Which of the five pieces in the answers fits with the piece in the separate picture, so that together they form a rectangle ?

In the Adventure Park, 30 children took part in two of the adventures. 15 of them participated in the “ moving bridge” contest, and 20 of them went down the zip-wire. How many of the children took part in both adventures ?

Schoolmates Andy, Betty, Cathie and Dannie were born in the same year. Their birthdays were on February 20^th, April 12^th, May 12^th and May 25^th, not necessarily in this order. Betty and Andy were born in the same month. Andy and Cathie were born in the same day of different months. Who of these schoolmates is the oldest ?

On the map, white lines represent streets. There are pictograms on some intersections ( for example, trafic light, basket, tram ). Ann started walking at the beginning of the middle vertical street in the direction of the arrow. At every intersection of streets she turned either to the right or to the left. First she turned right, then left, then again left, then right, then left, and finally again left. Which of the landmarks did An approach in the end ?