IMAS 2013 — Middle Primary Grades 3–4 — Round 2

The diagram shows an aquarium containing five starfish, each occupying a labelled compartment. Water is pumped into the aquarium through the pipe on the left side. Which compartment is the first to be flooded with water?

When 10101 is subtracted from 10000000, how many times does the digit 9 appear in the difference?

What is the sum of 32 copies of 1000, 19 copies of 100 and 29 copies of 10?

The diagram shows a $ 6 \times 8 $ chessboard with squares painted in black and white in an unusual pattern. Starting from the top left corner, a marker must move between squares which have opposite colours and share a common border. What is the minimum number of black squares it must visit in order to arrive at the top right corner, counting it as one of the black squares visited?

Max gives 27 apples to a group of friends. The numbers of apples they receive are consecutive positive integers. What is the maximum size of this group?

When the digits 0, 1, 2, 5, 6, 8 and 9 are rotated $ 180^{\circ} $, they become 0, 1, 2, 5, 9, 8 and 6 respectively. What does 9105 become when the four-digit number is rotated $ 180^{\circ} $?

An ant by itself is unable to drag a slice of bread back to the anthill. So summons 9 other ants to help, but the slice is still too heavy. So each of these 10 ants summons 9 other ants to help, and they manage to drag the slice back to the anthill. How many ants are involved?

Lily has 100 chocolates. She eats one on the first day. Each day after, she eats twice as many as the day before, until all the chocolates have been eaten. How many chocolates did she eat on the last day?

A class is putting up 10 rectangular posters of the same shape and size on a wall. Each poster must be held in place by one nail near each corner. Adjacent posters may overlap slightly so that the same nail can serve to hold both of them. The diagram shows how 9 nails can hold four posters adjacent diagonally. What is the minimum number of nails required to hold all 10 posters?

The diagram shows seven marked points, six on a semicircular arc, including both endpoints of the diameter, along with the centre of the arc. How many triangles are there whose vertices are all chosen from these points?

The diagram shows an addition of a three-digit number, a two-digit number and a one-digit number, with a three-digit sum. The same letter stands for the same digit and different letters stand for different digits. A question mark can stand for any digit, including those represented by a letter. What is the maximum value of the sum?

$$ \begin{array}{r} X\quad Y\quad Z\\ Y\quad Z\\ +\quad Z\\ ?\quad?\quad?\end{array} $$

Leon uses a code to convert a letter string consisting only of As, Bs and Cs, into a number string consisting only of 0s and 1s, by replacing A with 101, B with 11 and C with 0. If the number string obtained is 110101101110101, what is the number of letters in the original letter string?

The total number of players on three badminton teams is 29. No two players on the same team play against each other, while every two players on different teams play each other exactly once. What is the maximum number of games played?

Some of the squares in the $ 6 \times 6 $ table are shaded. The numbers of shaded squares in the respective rows and columns are indicated on the edge of the table, and there are no gaps between the shaded squares in any row or column. Show where the shaded squares are.

A three-digit number is 13 times the product of its digits. The hundreds digit is larger than either of the other two digits. What is this number?