A rook starts just before cell 1 on the numbered strip. Each move takes it 4 or 7 cells to the right, as shown. Which numbered cell can it NOT land on?
Practice scoring for this whole 16-question paper: 1 point per correct answer, 0 if wrong or blank, maximum 16. These equal weights are editorial because no numerical marks are printed on the individual source paper.
The caterpillar and butterfly represent natural numbers. Following the operations in the diagram, find the caterpillar’s number if the butterfly is the largest two-digit even number.
Black ants are marching in a line. Two red ants join next to each other, as shown. The number of black ants in front of them is three times the number behind them. Which could be the total number of ants in the new line?
Jane rotates the coloured square clockwise by a quarter-turn, from Figure 1 to Figure 2 as shown. If she rotates Figure 2 another 22 times in the same way, which option results?
Figure 1 and Figure 2 label the two starting arrangements. Rotate 1 time means one clockwise quarter-turn; Rotate another 22 times starts from Figure 2. R, G, B and Y identify the red, green, blue/purple and yellow cells.
Henry folds a square sheet in half twice along the shown diagonal folds, then makes the two cuts indicated by the scissors. How many pieces does he obtain?
In an eating contest, each person must eat 10 burgers. The bar graph shows their finishing times. The second person to finish is 12 minutes faster than the last person. How many minutes does the winner take to eat all 10 burgers?
Minutes labels the vertical time axis; People labels the horizontal axis.
Fred and Peter play a game in which the winner gains 5 points and the loser loses 2 points. There are no ties. Fred wins exactly 18 games and Peter finishes with 134 points. How many games do they play in total?
Kellie arranges four identical small squares in a row to make a rectangle. Kyle rearranges them into a large square, as shown. Kyle’s shape has perimeter 10 cm less than Kellie’s. Find the perimeter of one small square.
Andrea has 10 cards. On one side she writes consecutive odd numbers starting at 11, one on each card. On the other side she writes consecutive even numbers starting at 26. Find the sum of all the numbers on both sides of the cards.
Lucy glues 14 white cubes of side length 3 cm into the shown shape. She paints every outside surface yellow except the bottom. Find the total painted area.
A box contains 121 balls numbered consecutively from 25 to 145. What is the least number that must be drawn without looking to guarantee two balls whose numbers differ by 18?
James places nine consecutive odd numbers in the magic square shown so that every row, column and diagonal has the same sum. Some entries are letters. Find A + E.
A square grid of 1 small square uses 4 matches; a grid of 4 small squares uses 12 matches; a grid of 9 small squares uses 24 matches. Following the same pattern, a grid uses 180 matches. How many small squares does it contain?
Scoring note: the source labels this question Star of hope. This historical 16-question paper prints no numerical scoring rule. The package uses the same editorial practice value of 1 point as every other question, with no deductions; it does not claim official historical scoring.
