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If 5 cats can catch 5 mice in 5 minutes, how many cats are required to catch 100 mice in 100 minutes?
A full glass of water weighs 400 grams. An empty glass weighs 100 grams. How much does a half-full glass of water weigh?
Fran has four dogs whose ages are 3, 4, 5 and 6 years. She feeds them one at a time according to the rule that a younger dog can never eat right before a dog that is only one year older. In how many different orders can Fran feed her four dogs?
Hannes has a game board with 11 spaces. He places one coin each on eight spaces that lie next to each other. He can choose on which space to place his first coin. No matter where Hannes starts some spaces will definitely be filled. How many spaces will definitely be filled?
A mouse wants to escape a labyrinth. On her way out she is only allowed to go through each opening once at most. How many different ways can the mouse choose to go to get outside?
How many triangles are there in this picture?
Grandma stands in the courtyard calling her cat and all her chickens. After a little while 20 legs are running towards her. How many chickens does Grandma have?
A snail is at the bottom of a well 20 yards deep. Every day it climbs 7 yards and every night it slides back 4 yards. In how many days will it be out of the well?
Susi makes this pattern using ice-lolly sticks. Each stick is 5 cm long and 1 cm wide. How long is Susi’s pattern?
The giants Tim and Tom build a sandcastle and decorate it with a flag. They insert half the flagpole into the highest point of the sandcastle. The highest point of the flagpole is now 16 m above the floor, the lowest 6 m (see diagram). How high is the sandcastle?
The floor of a room is covered with equally big rectangular tiles (see picture). How long is the room?
Two equal trains, each with 31 numbered wagons, travel in opposite directions. When the wagon number 7 of a train is side by side with the wagon number 12 of the other train, which wagon is side by side with the wagon number 11?
Whenever the kangaroo goes up seven steps, the rabbit goes down three steps. When the kangaroo is on step number 56, on which step will the rabbit be?
The diagram below shows three different two-dimensional views of a transparent cube wrapped with a piece of thick wire. Which of the five cubes is it?
Tick, Trick and Track are triplets. Their brother Franz is exactly 3 years older. All four children are having their birthdays today. How old can the four brothers be altogether?
Together Paul and Josef are 12 years old. How old will they both be together in four years time?
Place the numbers 1–6 in the six circles below so the sum of each side of the triangle is 12. One of the numbers has be placed for you. Which number is placed in the red circle? (The numbers may be used once only.)
In the addition problem below, the letters AB represent a two-digit number. If you know that the letter B is not a zero (0), can you tell me which number represent A?
Place the numbers 1–12 in the twelve circles below so the sum of each side of the triangle is 36. Some of the numbers have be placed for you. Which number is placed in the red square? (The numbers may be used once only.)
A boy says, “I have as many brothers as sisters.” His sister says, “I have twice as many brothers as sisters.” How many brothers and sisters are there in this family?
Leo and Max are standing in a queue that is made up of 11 people in total. There are 7 people in front of Leo, Max stands directly behind him in the queue. How many people are behind Max?
Four of the numbers 1, 3, 4, 5 and 7 are written into the boxes so that the calculation is correct. Which number was not used?
The road from Anna’s to Mary’s house is 16 km long. The road from Mary’s to John’s house is 20 km long. The road from the crossing to Mary’s house is 9 km long. How long is the road from Anna’s to John’s house?
Together the three squirrels Anni, Asia and Elli have 10 nuts. Each one has a different number of nuts but at least 2 nuts. Anni has the least number of nuts. Asia has the most nuts. How many nuts does Elli have?
Maia the bee can only walk on colorful houses. How many ways can you color exactly three white houses with the same color so that Maia can walk from A to B?
In the figure, an arrow pointing from one person to another means that the first person is shorter than the second. For example, person B is shorter than person A. Which person is the tallest?
Rita numbered the circles of the figure from 1 to 8, so that the sum of the three numbers on each of the four sides of the square equals 13. What is the sum of the four numbers written on the colored circles?
Six different numbers, chosen from integers 1 to 9, are written on the faces of a cube, one number per face. The sum of the numbers on each pair of opposite faces is always the same. Which of the following numbers could have been written on the opposite side with the number 8?
Tania bought 14 chocolates, 8 of them round and the rest square. Half were white chocolates and half were dark chocolates. Among the square chocolates, only two are not white. How many dark round chocolates did Tania buy?
Cynthia paints each region of the figure in a single color: red, blue or yellow. She paints with different colors the regions that touch each other. In how many different ways can Cyntia paint the figure?
A card has a diagram printed on one side and the other side is plain white. The card is first flipped over to the left and then upwards (see diagram). Which picture do you get this way?
Konrad has some pieces of cardboard which all look like this: Which of the shapes below can he not make out of these pieces?
Alfred turns his building block 10 times. The first three times can be seen in the picture. What is the final position of the building block?
Alton and Beatrice live in the same neighborhood and go to the same cupcake shop. Beatrice lives 5 blocks closer to the cupcake shon than Alton does. What is the minimum possible distance between Alton’s house and Beatrice’s house? Assume all distances are positive whole numbers.
A farmer has 6 roosters. He buys some fencing so that he can make separate pens for the roosters. What is the minimum number of lengths that he needs to create 6 separate pens? (Assume that the fencing must attach at their ends.)
There are white, blue and black squares. Three children use these to make this pattern. First Anni replaces all black squares with white squares. Then Bob replaces all blue squares with black squares. Finally Chris replaces all white squares with blue squares. Which picture have the three children now created?
Maria made a block using white cubes and colored cubes in equal amounts. How many of the white cubes cannot be seen in the picture?
Julia drew the picture on the side of a cardboard sheet, cut, folded and glued to form a cube. Which of the cubes below can be the one she did?
Amelia built a crown using 10 copies of pentagon piece. The parts were joined together so that the sides in contact had the same number, as shown in the picture, where four parts are visible. What is the number that appears in the colored triangle?
Which net will form this shape?
Janaína made the construction on a grid, using some lighted colored cubes and others darker. Looking from above the construction, what can she see?
Stan has five toys: a ball, a set of blocks, a game, a puzzle and a car. He puts each toy on a different shelf of the bookcase. The ball is higher than the blocks and lower than the car. The game is directly above the ball. On which shelf can the puzzle not be placed?
Steven wants to write each of the digits 2, 0, 1 and 9 into the boxes of following addition. He wants to obtain the biggest result possible. Which digit does he have to use for the single-digit number?
One of the 5 children Alex, Bartek, Cora, Dani and Emil has eaten a cake. One of the children lies. Which child has eaten a cake?
Each of the 5 boxes contains either apples or bananas, but not both. The total weight of all the bananas is 3 times the weight of all the apples. Which boxes contain apples?
Martin placed 3 different types of objects, hexagons, squares and triangles, on sets of scales, as shown. What does he need to put on the left-hand side on the third set of scales for these scales to balance?
The picture shows the five houses of five friends and their school. To go to school, Doris and Ali walk past Leo’s house. Eva walks past Chole’s house. Which is Eva’s house?
The cards 2, 3, 4, 5 and 6 are placed into 2 boxes. The sums of the numbers in each box are the same. Which number must be in the box with the number 4?
Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?
The numbers 1 to 9 are placed in the squares shown with a number in each square. The sums of all pairs of neighbouring numbers are shown. Which number is placed in the shaded square?
Mia throws darts at balloons worth 3, 9, 13, 14 and 18 points. She scores 30 points in total. Which balloon does Mia definitely hit?
The kangaroo had two branches for lunch. Each branch had 10 leaves. The kangaroo ate some leaves from one branch. Then, from the second branch, it ate as many leaves as were left on the first branch. How many leaves in total were left on the two branches?
In an ice cream shop there is some money in a drawer. After 6 ice creams were sold, there were 70 euros left in the drawer. After a total of 16 ice creams were sold, there were 120 euros left in the drawer. How many euros were there in the drawer at the start?
Edmund cut a ribbon as shown in the picture. How many pieces of the ribbon did he finish with?
The picture beside shows two cogs, each with a black tooth. Where will the black teeth be after the small cog has made one full turn?
Kangie eats only apples on Monday, Wednesday and Friday. On Tuesdays and Thursdays he eats only mangoes. He eats either 2 apples or 3 mangoes a day. On Saturdays and Sundays he eats nothing. How many pieces of fruit does Kangie eat in two weeks?
A hallway has the dimensions shown in the picture. A cat walks on the dashed line along the middle of the hallway. How many meters does the cat walk?
Linda fixes 3 photos on a pin board next to each other. She uses 8 pins to do so. Peter wants to fix 7 photos in the same way. How many pins does he need for that?
Anna uses 32 small red squares to frame a 7 cm by 7 cm big picture. How many small red squares does she have to use to frame a 10 cm by 10 cm big picture?
Five boys competed in a shooting challenge. Ricky scored the most points. Which target was Ricky’s?
Gaspar has these seven different pieces, formed by equal little squares. He uses all these pieces to assemble rectangles with different perimeters, that is, with different shapes. How many different perimeters can he find?
Paulo took a rectangular sheet of paper, yellow on one side and green on the other side and, with several folds shown in the dotted lines in the figure below, made a little paper plane. To give the airplane a charm, Paulo made a circular hole, marked on the last figure.
A kangaroo laid out 3 sticks like this to make a shape. It is not allowed to break or to bend the sticks. Which shape could the kangaroo make?
Four identical pieces of paper are placed as shown. Michael wants to punch a hole that goes through all four pieces. At which point should Michael punch the hole?
Which figure can be made from the 2 pieces shown on the right?
Mara built the square by using 4 of the following 5 shapes. Which shape was not used?
ABCD is a rectangle whose area is 12 square units. How many square units are contained in the area of trapezoid EFBA?
Rectangle ABCD is inscribed in a semicircle with diameter FE, as shown in the figure. Let DA=16 and let FD=AE=9. What is the area of ABCD?
There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that point Q is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?
Zara has a collection of marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?
How many integers between and have four distinct digits arranged in increasing order? (For example, 2347 is one integer.)
A dartboard consists of three concentric circles with radii 10, 5 and 1, respectively, measured in inches. If a thrown dart is guaranteed to hit the board, but its position on the board is uniformly random, what is the probability that it lands in the yellow portion of the board?
The first four stages of a dot pattern are shown. How many more dots are in the figure at Stage 47 than in the figure at Stage 27?
If two distinct ellipses and a square are drawn, what is the maximum possible number of points at which at least two of the three planar figures intersect?
Sides DL and AN in a regular hexagon DANIEL, shown here, are extended until they intersect at a point F. If the sides of the hexagon have length 6 units, what is the length of segment FE? Express your answer as a radical in simplest form.
In right triangle ABC, with AB = 44 cm and BC = 33 cm, point D lies on side BC so that BD:DC = 2:1. If vertex A is folded onto point D to create quadrilateral BCEF, as shown, what is the area of triangle CDE?
Bob has 40 cents in his pocket. If Bob has no pennies, how many different combinations of quarters, dimes and/or nickels could he have?
In this conversation shown between Anne and Diana, if Diana is correct, what is the greatest possible value of X?
How many more quadrilaterals than triangles are in the figure shown?
The figure shows a solid composed of 32 unit cubes. What is the least number of unit cubes that can be added to this figure to create a solid that is a cube?
A large cube has side-length 7cm. On each of its 6 faces, the two diagonals are drawn in red. The large cube is then cut into small cubes with side-length 1cm. How many small cubes will have at least one red line drawn on it?
Each shelf holds a total of 64 deciliters of apple juice. The bottles have three different sizes: large, medium and small. How many deciliters of apple juice does a medium bottle contain?
Which of the pieces of fruit is the heaviest?
Ann, Bob, Carina, Dan and Ed are sitting at a round table. Ann is not next to Bob, Dan is next to Ed and Bob is not next to Dan. Which two people are sitting next to Carina?
Five squares are positioned as shown. The small square indicated has area 1. What is the value of ℎ?
The diagram shows 3 hexagons with numbers at their vertices, but some numbers are invisible. The sum of the 6 numbers around each hexagon is 30. What is the number on the vertex marked with a question mark?
The number 5021972970 is written on a sheet of paper. Julian cuts the sheet twice, so he gets 3 numbers. What is the smallest sum he can get by adding these 3 numbers?
A box contains only green, red, blue and yellow counters. There is always at least one green counter amongst any 27 counters chosen from the box; always at least one red counter amongst any 25 counters chosen; always at least one blue amongst any 22 counters chosen and always at least one yellow amongst any 17 counters chosen. What is the largest number of counters that could be in the box?
The 6-digit number 2ABCDE is multiplied by 3 and the result is the 6-digit number ABCDE2. What is the sum of the digits of this number?
In a particular fraction the numerator and denominator are both positive. The numerator of this fraction is increased by 40%. By what percentage should its denominator be decreased so that the new fraction is double the original fraction?
A set S contains some, but not all, of the positive integers from 3 to 7. Some statements describing S are given below. The statement numbered n is true if the number n is in S and false if n is not in S. What is the product of the numbers that are in S?
How many pairs of numbers (a, b) satisfy rules I and II shown here?
Starting at the top and selecting paths randomly as you move downward, what is the probability of ending at an odd number? Express your answer as a common fraction.
There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We coloured 1/8 of the large square. Which one is our coloring?
Emilio started a job on July 1, 2000 at a salary of $40,000. If he got an increase of 10% each year, in what year did his salary first exceed $80,000?
Square ABCD has sides of length 12 cm. The three interior segments divide the square, as shown, into two congruent trapezoids and an isosceles triangle, all with equal areas. What is the length of segment CF?
How many squares can be drawn using only dots in this grid of 16 evenly spaced dots as vertices?
Currently, the sum of the ages of Yumi, Rana and Victoria is 42 years. Four years ago, the sum of the ages of Rana and Victoria was equal to the current age of Yumi. What is Yumi’s current age?
Debbie has equal numbers of dimes and quarters with a total value of $1.40. How many coins does she have altogether?
Rob has 10 white, 8 red and 6 blue socks in his drawer. If he selects socks from the drawer randomly, without looking, what is the least number of socks Rob must select to guarantee that he has removed a pair of white socks?
Bob folds a piece of paper, then punches a hole into the paper and unfolds it again. The unfolded paper then looks like the picture below (see diagram). Along which dotted line has Bob folded the paper beforehand?
Fill in the same number in the position of each car to make the formula stand. What’s this number?
Five square cards are stacked on a table, as shown. The cards are removed one by one from the top of the stack. In what order are the cards removed?
Each one of the 5 keys locks exactly one padlock. Every letter on a padlock stands for exactly one digit, same letters mean same digits. Which digits are on the key with the question mark?
A big cube is made up of 9 identical building blocks. Each building block looks like the image below. Which big cube is possible?
The 10 islands are connected by12 bridges (see diagram). All bridges are open for traffic. What is the minimum number of bridges that need to be closed off, so that the traffic between A and B comes to a halt?
Taro glanced at me and went to the 1:30 appointment. He thought he could make it 5 minutes earlier, but he was 10 minutes late. How slow am I?
Sofie wants to pick 5 different shapes from the boxes. She can only pick 1 shape from each box. Which shape must she pick from box 4?
There are 53 residents living in the apartment. How many people live on the third floor?
18 cubes are coloured white or blue or green and are arranged as shown. The figures below show the white and the blue parts. Which of the following is the green part?
Diana first got 6 points with three arrows on the target, as on the left picture. The second time she got 8 points, as in the middle picture. How many points did she get the third time?
Four strips are woven into a pattern, as shown above. What do you see when you look at it from the other side?
Old McDonald has a horse, two cows and three pigs. How many more cows does he need, so that exactly half of all his animals are cows?
How many dots are there in the picture?
As shown in the figure, the large rectangle ABCD is made up of 8 identical small rectangles spliced together. It is known that the area of the large rectangle ABCD is 135 square centimeters. The area of the blue rectangle in the middle is 55 square centimeters. What is the width of the small rectangle in centimeters?
The structure in the figure below is made up of 8 square blocks linked together. What does it look like from the top?
The number shown in the figure below is 8. Knowing that the black dot represents 1, which figure represents 12?
Each square contains one of the numbers 1, 2, 3, 4, 5 or 6 and each number is used once. Except for the top row, the number in each square is the difference of the numbers in the two squares above it. What number is in the square marked A?
Jone and Daniel walked in different directions from the red dot, at the same speed. Where will they meet?
Square ABCD is composed of nine congruent squares as shown. The area of the shaded region is 14 square centimeters. What is the area of square ABCD, in sq cm?
A mouse and a cheese are in the opposite corners of the board.The mouse can only move as shown by the arrows. In how many ways can the mouse reach the cheese?
Each shape represents exactly one digit. The sum of the digits in each row is stated on the right hand-side of each row. Which digit does the star stand for?
How many white squares need to be colored in black, so that there are exactly twice as many white squares as there are black squares?
If you want the white and red areas to have the same area, which figure should be placed at the question mark?
Into how many pieces will the string be cut?
Each one of the four keys locks exactly one pad lock. Every letter on a padlock stands for exactly one digit. Same letters mean same digit s. Which letters must be written on the fourth padlock?
Rosana has some balls of 3 different colours. Balls of the same colour have the same weight. What is the weight of each white ball ?
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