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 Opposite faces of a normal dice add to what number? (number)
Show worked solution
7: 1↔6, 2↔5, 3↔4.
2 On a normal dice, what is opposite the 3? (number)
Show worked solution
3 + 4 = 7.
3 Can two squares that TOUCH on a net be opposite faces on the cube?
Show worked solution
No — touching squares share an edge and become neighbours.
Level 2 · Core
4 A net row reads 5-3-2-4. Which face is opposite the 5? (number)
Show worked solution
Skip-one along the row: 5 skips 3 to oppose 2.
5 A net row reads 5-3-2-4. Is this part of a NORMAL dice? (5 opposite 2 = 7 ✓; 3 opposite 4 = 7 ✓)
Show worked solution
Yes so far — both visible pairs sum to 7; the remaining pair (1, 6) must hang above and below.
6 A net shows 2 and 5 sharing an edge. Normal dice possible?
Show worked solution
No — 2 and 5 must be opposite (sum 7) but touching faces are neighbours. Forbidden touch!
Level 3 · Challenge
7 Row: 1-4-6-3, with 2 hanging above the 4 and 5 below the 4. Opposite pairs: 1-6, 4-3, 2-5. Normal dice?
Show worked solution
1+6 = 7 ✓, 4+3 = 7 ✓, 2+5 = 7 ✓ — yes, all three pairs check out.
8 Row: 1-2-6-4, with 3 above the 2 and 5 below the 2. Pairs: 1-6, 2-4, 3-5. Normal dice?
Show worked solution
No — 2 + 4 = 6 and 3 + 5 = 8. Only 1-6 works; one bad pair kills the net.
9 How many squares does a cube net have? (number)
Show worked solution
6 — one per face; arrangements differ but the count never does.