Cathy draws a square of area 100 cm². She joins the midpoints of the sides to make a smaller square. What is the area of the smaller square ? 

On Lisa’s refrigerator 8 strong magnets ( the black circles in the picture ) hold some postcards.

What is the greatest number of magnets Lisa could remove so that no postcard falls to the ground ?

Starting with 555 groups each containing 9 rocks we pile all these rocks together into one pile. We then divide this new pile into groups with 5 rocks each. How many new groups do we get ?

Mike cuts a pizza into quarters. Then he cuts every quarter into thirds. What part of the whole pizza is one of the pieces ?

Ahmed starts counting at the number 19 and keeps counting until 89. If he takes one second to say each number how long does it take to count all the numbers ?

A centipede has 25 pairs of shoes. It needs one shoe for each of its 100 feet. How many more shoes does the centipede need to buy ?

A fly has 6 legs, a spider has 8 legs. Together, 3 flies and 2 spiders have as many legs as 9 chickens and several cats. How many cats are there ?

Alice has 4 pieces of this shape: . Which picture can she not make from these four pieces ?

Kalle knows that 1111 x 1111 = 1234321. What is the answer of 1111 x 2222 ?

There are 10 islands and 12 bridges, as depicted in the figure. All bridges are open for traffic right now. What is the smallest number of bridges that must be closed in order to stop the traffic between A and B ?

Martin wants to colour the squares of the rectangle so that 1/3 of all squares are blue and half of all squares are yellow. The rest of the squares are to be coloured red.

When the car wheels make one full rotation the car moves forward by about 1.8 meters. Approximately how many kilometres will the car move forward after 10,000 full rotations of the wheels ?

There are 32 students in Mrs. Vicky’s class. Part of the students took one pencil each from the box with pencils on the teacher’s desk. Then a third of the remaining students took 3 pencils each, and there were no more pencils left in the box. How many pencils were there in the box at first ?

Three rhinoceroses Jane, Kate and Lynn go for a walk: Jane first, Kate in the middle, and Lynn-last. Jane weighs 500 kg more than Kate. Kate weighs 1000kg less than Lynn. Which of the following pictures may show Jane, Kate and Lynn in the order they walked ?

Peter and Nick are both working on “ Kangaroo” contest problems. For every two problems that Peter solves, Nick manages to solve three problems. In total, the boys solved 30 problems. How many problems did Nick solve more than Peter ?

Bob folded a piece of paper, used a hole puncher and punched exactly one hole in the folded paper. Then, he unfolded the piece of paper, which looked as shown below.

Which of the following pictures shows the lines along which Bob folded the piece of paper ?

A special die has a number on each of its six faces. The sums of the numbers on opposite faces are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face ?

Tom wrote all the numbers from 1 to 20 in a row and obtained the 31-digit number

1234567891011121314151617181920

Then he deleted 24 of the 31 digits, so that the remaining number was as large as possible

Which number was it .

Peter went hiking in the moutains for 5 days. He started on Monday and his last trip was on Friday. Each day he walked 2 km more than the day before. The total distance he walked during the five days was 70 km. What distance did Peter walk on Thurday ?

In a chocolate store, one chocolate costs 3 dollars. One day the store had a deal: “ Buy two and get a third one free” and Adam decided to take 49 chocolates. How much did he pay for the chocolates ?

Eight kangaroos stood in a line as shown in the diagram.

At some point, two kangaroos standing side by side and facing each other exchanged places by jumping past each other. This was repeated until no further jumps were possible.

The Modern Furniture store is selling sofas, loveseats, and chairs made from idential modular pieces as shown in the picture. Including the armrests, the width of the sofa is 220 cm and the width of the loveseat is 160 cm

What is the width of the chair ?

There are five padlocks and 5 keys-one for each of them ( see the figure ). The number code on each key has been modified into a letter code on the corresponding padlock. Equal digits have been replaced by the same letter, and different digits – by different letters. What is the number code on the fifth key ?

Boris has an amount of money and three magic wands that he can use only once. Wand A adds 1 dollar. Wand S subtracts 1 dollar. Wand D doubles the amount. In which order must he use these wands to obtain the largest amount of money ?

A vase weighs 600g when oe third of it is filled with water. The same vase weighs 800g when two thirds of it are filled with water. What is the weight of the vase when it is empty ?