IKMC 2012 - Grades 3-4 - Self-study

Basil wants to write MATHEMATICS on a sheet of paper. Different letters must have different colours, and identical letters must have the same colour. How many colours will he need?

In four of the five pictures the white area is equal to the grey area. In which picture are the two areas different?

Father hangs laundry on a clothesline using as few pegs as possible. For 3 towels he needs 4 pegs, as shown. How many pegs does he need for 9 towels?

Iljo colours squares A2, B1, B2, B3, B4, C3, D3 and D4 in the grid. Which colouring does he get?

13 children play hide and seek. One is the seeker and the others hide. After a while 9 children have been found. How many are still hiding?

Mike and Jake each threw three darts, as shown. Who won, and by how many points?

A regular rectangular wall pattern uses grey and striped tiles. Some have fallen off, as shown. How many grey tiles have fallen off?

2012 is a leap year, with 29 days in February. On 15 March 2012, grandfather’s ducklings are 20 days old. When did they hatch?

You have L-shaped tiles, each consisting of 4 squares as shown. How many of the four displayed shapes can be made by joining two of these tiles?

Three balloons cost 12 cents more than one balloon. How much does one balloon cost?

Grandmother made 20 gingerbread biscuits. She put raisins on 15 and nuts on 15. At least how many biscuits had both raisins and nuts?

In a sudoku, 1, 2, 3 and 4 occur exactly once in every row and column. Patrick first writes the results of the calculations, then completes the grid. What goes in the grey cell?

Among Nikolay’s classmates there are twice as many girls as boys. Which number can be the total number of children in this class?

At animal school there are 3 kittens, 4 ducklings, 2 goslings and several lambs. The owl teacher counts 44 pupil legs. How many lambs are there?

A cuboid is made of four pieces as shown. Each piece consists of four cubes and has one colour. What is the shape of the white piece?

Each of 15 Christmas-party tables has one candlestick. Six candlesticks have five branches; the others have three. How many candles are needed?

A grasshopper starts at ground level and can jump only 3 steps up or 4 steps down. What is the least number of jumps needed to rest on step 22?

Frank made a snake of seven dominoes with equal numbers of dots touching. The whole snake had 33 dots. George removed two tiles as shown. How many dots were in the place with the question mark?

Source note: the supplied diagram does not display its referenced question mark. The intended reading is the number on either of the two touching hidden halves.

Gregor uses the digits 1, 2, 3, 4, 5 and 6 exactly once to make two three-digit numbers, then adds them. What is the greatest possible sum?

Laura, Iggy, Val and Kate line up for a photo. Kate and Laura must be next to each other, and Iggy must stand next to Laura. In how many ways can they arrange themselves?