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 ?

A plane takes off from Vienna at 11:00 am local time and arrives in Toronto at 1:00 pm local time. On average, it takes 8 hours for a plane of this type to fly this distance. What time is it in Toronto when it is 7:00 am in Vienna ?

What is the greatest number N, which, when divided by 7, has a remainder that is equal to the quotient ?

The king and his messengers are travelling from the castle to the summer palace at the speed of 5 km/h. Along the way, the king sends a messenger back to the castle; and one hour later, he sends back another messenger. If the messengers travel at a speed of 10 km/h, what is the time between their arrivals at the castle ?

The 3 x 3 x 3 cube in the picture is made of 27 small cubes.

How many small cubes do you have to remove to see the following result when viewing from the right, from above, and from the front ?

Andy made a playlist 5 songs ( A, B, C, D and E ). Song A is 3 minutes long, song B is 2 minutes and 30 seconds, song C is 2 minutes, song D is 1 minute and 30 seconds, and song E is 4 minutes. The songs play in this order in a continuous loop. If Andy left the house when song C was just starting, what song was playing when he got back home 1 hour later ?

Dan entered the numbers from 1 to 9 in the cells of a  3 x 3 table. He began by placing the numbers 1, 2, 3 and 4 as shown in the picture:

It so happened that for the number 5, the sum of the numbers in the adjacent cells ( having a common side ) was equal to 9. What is the sum of the numbers adjacent to the number 6 ?

Rabbit Vasya loves cabbage and carrots. In a day, he eats either 9 carrots, or 2 heads of cabbage, or I head of cabbage and 4 carrots. But some days he only eats grass. Over the last 10 days, Vasya ate a total of 30 carrots and 9 heads of cabbage. On how many of these 10 days did he eat only grass ?

Trees grow on only one side of Park Avenue. There are 60 trees in total. Every second tree is a maple, and every third tree is either a linden or a maple. The remaining trees are birches. How many birches are there ?

Granny has 10 grandchildren, all of different ages. Alice is the eldest. The sum of the ages of all grandchildren is 180. At least how old is Alice ?

A thin colourful ribbon is stuck on a transparent plastic cube ( see the picture ).

Which of the following pictures does not represent the cube as seen from any perpective ?

Bob is going to visit four cities. He will start from and end up in his home town. The figure shows a map of the regions with the cities. The roads are only along the grid lines.

Bob wants to make the trip as short as possible. Which route should Bob follow ?

A rectangle with a perimeter of 34 cm was divided into two smaller rectangles with perimeters 28 cm and 30 cm, as shown in the figure.

What is the are of the big rectangle ?

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 ?