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HKIMO 2026 Grade 3 National Final (Heat) Set 05

Question 1

There are 27 transparent boxes as in Figure 1. Each layer contains 9 boxes as in Figure 2. Black marbles are placed inside; the top, front and right views are shown. How many marbles are there?

Editorial box convention: each small box contains at most one marble, centred in that box. A black dot in a view means at least one marble lies on that line of sight; overlapping marbles appear as one dot. The source does not explicitly state the per-box capacity.

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Question 2

According to the pattern, counting from the left, how many circles occur among the first 100 figures?

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Question 3

What number replaces the question mark in the table?

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Question 4

Peter uses 4 straight lines to cut a rectangle into parts. At most how many parts can he get?

Question 5

According to the pattern, how many triangles are in the fourth group?

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Question 11

Hermione has 37 oranges and Harry has 13. How many must Hermione give Harry so that Harry has 4 times as many as Hermione?

Question 13

Find the next term in the pattern: $2,7,22,67,202,607,1822,\ldots$

Question 15

What is the smallest 3-digit number divisible by both 2 and 3?

Question 17

Harry stacks identical cubes as shown. At least how many cubes are in the figure?

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Question 19

Five points are shown. How many straight lines link every point with every other point?

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