IKMC 2016 - Grades 5-6 - Self-study

Which of the following traffic signs has the largest number of lines of symmetry?

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

A thread of length 10 cm is folded into equal parts as shown in the figure. The thread is cut at the two marked places. What are the lengths of the three parts?

On Lisa's refrigerator 8 strong magnets hold some postcards. What is the largest number of magnets that she could remove so that no postcard falls to the ground?

Cathy draws a square with side length 10 cm. She joins the midpoints of the sides to make a smaller square. What is the area of the smaller square?

Alice's mother wants to see a knife on the right side of each plate and a fork on the left side. How many interchanges of a knife and fork does Alice need to make in order to please her mother?

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?

Tom and John build rectangular boxes using the same number of identical cubes. Tom's box and the first level of John's box are shown. How many levels will John's box have?

On the left side of the room, Bea and Pia are sleeping with their heads on their pillows facing each other. On the right side of the room, Mary and Karen are sleeping with their heads on their pillows with their backs to each other. How many girls are sleeping with their right ear on the pillow?

The piece of paper shown is folded along the dotted lines to make an open box. The box is put on a table with the top open. Which face is at the bottom of the box?

Which of the following figures cannot be formed by gluing these two identical squares of paper together?

Mary, Ann, and Nata work in a kindergarten. Each day from Monday to Friday exactly two of them come to work. Mary works 3 days per week and Ann works 4 days per week. How many days per week does Nata work?

Five squirrels A, B, C, D and E are sitting on the line. They pick 6 nuts marked by crosses. At one moment the squirrels start running to the nearest nut at the same speed. As soon as a squirrel picks a nut, it starts running to the next closest nut. Which squirrel will get two nuts?

There are 30 students in a class. They sit by pairs so that each boy is sitting with a girl, and exactly half of the girls are sitting with a boy. How many boys are there in the class?

The number 2581953764 is written on a strip of paper. John cuts the strip 2 times and gets 3 numbers. Then he adds these 3 numbers. Which is the smallest possible sum he can get?

Bart is getting his hair cut. When he looks in the mirror the clock looks like this. What would he have seen if he had looked in the mirror ten minutes earlier?

Grandmother bought enough catfood for her four cats to last for 12 days. On her way home she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the catfood last?

Each letter in BENJAMIN represents one of the digits 1, 2, 3, 4, 5, 6 or 7. Different letters represent different digits. The number BENJAMIN is odd and divisible by 3. Which digit corresponds to N?

Tim, Tom and Jim are triplets, while their brother Carl is 3 years younger. Which of the following numbers could be the sum of the ages of the four brothers?

The perimeter of the rectangle ABCD is 30 cm. Three other rectangles are placed so that their centres are at the points A, B and D (see the figure). The sum of their perimeters is 20 cm. What is the total length of the thick line?