Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 How many faces does one cube have?
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A cube has 6 faces.
2 Three cubes are glued in a row. Looking from every direction, how many faces can be seen?
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18 − 4 = 14 faces can be seen.
3 Twelve loose cubes are used to build objects that each need 4 cubes. How many objects can be built?
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12 ÷ 4 = 3 objects.
Level 2 · Core
4 This object has no floating cubes and no hidden gaps. How many cubes is it made of?
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Base: 4 cubes. Two cubes on top of the back row: 2. Total 6, even though one base cube is almost hidden.
5 Five identical cubes are glued in a straight row. The row can be picked up and viewed from any direction. How many faces can NOT be seen?
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A row of 5 has 4 joins; each hides 2 faces: 8 hidden (22 visible of 30).
6 Two objects made of 7 and 9 identical cubes are broken into loose cubes. How many objects that each need 5 cubes can be made?
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7 + 9 = 16. 16 ÷ 5 = 3 remainder 1, so 3 objects.
Level 3 · Challenge
7 Three blocks measure 3 × 4 × 5 cm, 2 × 2 × 6 cm and 1 × 5 × 5 cm. Each can be turned any way. What is the tallest stack of all three, in cm?
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5 + 6 + 5 = 16 cm.
8 A 2 × 2 × 2 cube of 8 small cubes shows 24 faces. It is split into two flat 2 × 2 slabs of 4 cubes. How many faces can now be seen altogether?
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Each slab: 24 faces − 2 × 4 joins = 16 visible. Two slabs: 32. (Four joins were broken: 24 + 8 = 32.)
9 Two 2 × 2 × 2 cubes (8 small cubes each) are glued face to face to make one 2 × 2 × 4 block. How many small-cube faces can be seen on the block?
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24 + 24 = 48 faces showing before gluing. The glued patch hides 4 faces on each cube: 48 − 8 = 40. Check: a 2 × 2 × 4 block has surface 4 + 4 + 8 + 8 + 8 + 8 = 40.