Square paper sheets of two neighbouring houses together are inhabited by at most six people. What is the largest number of people that could be living on Jump Street ?

In a bag there are 3 green apples, 5 yellow apples, 7 green pears and 2 yellow pears. Simon randomly is taking fruits out of the bag one by one. How many fruits must he take out in order to be certain that he has at least one apple and one pear of the same colour ?

Two cats, Tom and Bob, caught together 42 mice in three days. Each day, Tom caught twice as many mice as in the previous day, while Bob caught two more mice than in the previous day. Nonetheless, both cats caught the same number of mice for the three days. How many mice did Tom and Bob catch together during the first day ?

Five children were standing in a line and holding 37 balloons in total. All children who were to the right of Andrew had together 14 balloons; all children standing to the right of Bob has together 32 balloons; the ones to the right of Clara – a total of 20 balloons, and to the right of Danny – 8 balloons. How many balloons did Clara hold ?

Mary wrote a number on each face  of a cube. Then, for each vertex, she added the numbers on the three faces sharing that vertex ( for example, for vertex B she added the numbers on faces BCDA, BAEF and BFGC ). The numbers computed by Mary for vertices C, D and E were 14, 16 and 24, respectively. What number did she compute for vertex F ?

A train has 12 coaches. Each coach has the same number of compartments. Mike is travelling in the third coach and in the 18^th compartment from the engine. Jane sat in the 7^th coach in the 50^th compartment from the engine. How many compartments are there in each coach ?

In how many ways can you place the three kangaroos in three different cells, out of the seven cells belows, so that not two kangaroos are neighbours ?

Four points lie on a line. The distances between them are, in increasing order:

2, 3, k, 11, 12, 14. What is the value of k ?

Basil used small cubes with side 1 to construct a cube with side 4. After that, he painted 3 faces of the big cube red and the other 3 faces blue. After he finished, there was no small cube with 3 red faces. How many small cubes have botth red and blue faces ?

Eugenie folded a round sheet of paper in half, three times, along the dotted lines, as shown in a, b and c below.

Then she cut the folded paper along the marked line, parallel to the folding line, as shown to the right.

Finally, Eugenie unfolded the paper. What shape did she obtain ?

Which of the weights are going upwards when the lower left wheel is turned clockwise as indicated ?

We want to insert the numbers 1, 2, 3, 4, 5, 6, 8 and 9 into the empty boxes below so that the sum of the numbers in each row, in each column, and in both the diagonals adds up to the same amount. What is the sum of the four numbers in the shaded boxes ?

Two three – digit numbers have all their six digits distinct. The first digit of the second number is twice the last digit of the first number. What is the smallest possible sum of two such numbers ?

A little Kangaroo is playing with his calculator allowing only operations on integers with an integer result. He starts with the number 12. He multiplies or divides the number by 2 or 3 ( if possible ) 60 times in a row. Which of the following results cannot be obtained ?