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 A machine adds 7. You put in 15. What comes out?
Show worked solution
15 + 7 = 22.
2 A machine doubles. Something came out as 18. What went in?
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Half of 18 is 9. (9 doubled is 18.)
3 A machine subtracts 12. You put in 40. What comes out?
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40 − 12 = 28.
Level 2 · Core
4 A machine multiplies by 4. Something came out as 52. What went in?
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52 ÷ 4 = 13.
5 A machine follows the rule "times 3, then add 2". You put in 7. What comes out?
Show worked solution
7 × 3 = 21, then 21 + 2 = 23.
6 A machine follows "add 5, then double". You put in 6. What comes out?
Show worked solution
6 + 5 = 11, then 11 doubled is 22.
Level 3 · Challenge
7 A machine follows "times 3, then subtract 5". Something came out as 40. What went in?
Show worked solution
Undo the − 5: 40 + 5 = 45. Undo the × 3: 45 ÷ 3 = 15. (Check: 15 × 3 − 5 = 40.)
8 A machine follows "halve, then add 8". Something came out as 20. What went in?
Show worked solution
Undo the + 8: 20 − 8 = 12. Undo the halving: 12 × 2 = 24.
9 Two machines run one after the other: the first adds 4, the second multiplies by 2. You put in 6 and the answer is 20. If you swap the machines round, what comes out from the same 6?
Show worked solution
Swapped: 6 × 2 = 12, then 12 + 4 = 16. Order changes the answer.