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 turns 1 into 4, 2 into 7 and 3 into 10. What does it turn 4 into?
Show worked solution
4 × 3 + 1 = 13.
2 A machine multiplies by 4 and then adds 1. Write what it turns 2 into, and what it turns 5 into.
Show worked solution
2 × 4 + 1 = 9 and 5 × 4 + 1 = 21.
3 What is the next number in the sequence 1, 2, 5, 10, 17?
Show worked solution
The gaps are the odd numbers, so the next gap is 9 and 17 + 9 = 26.
Level 2 · Core
4 In this square the rule works across the rows and down the columns. What replaces the star?
Show worked solution
Row 1: 2 × 3 = 6. Row 2: 4 × 5 = 20, so the middle is 5. Columns: 2 × 4 = 8 and 3 × 5 = 15, so the star is 8 × 15 = 120 — and 6 × 20 = 120 agrees.
5 A machine turns 1 into 5, 2 into 8 and 3 into 11. Write the number it multiplies by, and the number it then adds.
Show worked solution
Multiply by 3 and add 2: 1 → 5, 2 → 8, 3 → 11.
6 What is the next number in the sequence 3, 4, 7, 12, 19?
Show worked solution
The next gap is 9, so 19 + 9 = 28.
Level 3 · Challenge
7 Look at the sequence 2, 3, 6, 11, 18.1 The gaps increase by 2 each time.
2 The rule is "double the number before".
3 The next number is 27.
Which statements are correct?
2 The rule is "double the number before".
3 The next number is 27.
Which statements are correct?
Show worked solution
The gaps are 1, 3, 5, 7, each 2 more than the last (1 ✓). Doubling would send 2 to 4, not 3 (2 ✗). The next gap is 9, so 18 + 9 = 27 (3 ✓). 1 and 3.
8 A machine follows the rule "multiply by 3, then subtract 2". Write what it turns 4 into, and the input that produces an output of 25.
Show worked solution
4 × 3 − 2 = 10. Going backwards, 25 + 2 = 27 and 27 ÷ 3 = 9.
9 In a square where each row and each column multiplies, the top row is 2, 5 and 10, and the middle row starts with 3. What number is in the bottom-left cell?
Show worked solution
The first column multiplies: 2 × 3 = 6.