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 One row of a magic square is 8, 1, 6. What is the total of every line?
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8 + 1 + 6 = 15.
2 The total of every line is 15. Fill the two blanks.
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Middle row: 15 − 3 − 5 = 7. Middle column: 15 − 1 − 5 = 9.
3 Each term is the sum of the previous two: 1, 1, 2, 3, 5, 8, ?. What is the next term?
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5 + 8 = 13.
Level 2 · Core
4 Every line adds to the same total. What number is ◆?
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Total 21, centre 7, ◆ = 21 − 10 − 7 = 4.
5 Each term is the sum of the previous two. Fill the blanks.
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4 + 7 = 11; 7 + 11 = 18; check 11 + 18 = 29 ✓.
6 Each term is the sum of the previous three: 1, 2, 3, 6, 11, ?. What is the next term?
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3 + 6 + 11 = 20.
Level 3 · Challenge
7 Each term is the sum of the previous three.1 X = 2.
2 Y = 4.
3 Z = 12.
Which statements are correct?
2 Y = 4.
3 Z = 12.
Which statements are correct?
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Y = X + 2 and X + Y = 6, so X = 2 (1 ✓) and Y = 4 (2 ✓). Z = 0 + 4 + 6 = 10, not 12 (3 ✗). 1 and 2.
8 A magic square has a total of 51 and a centre of 17. One corner is 20, and the middle of the bottom row is 19.What is the corner opposite the 20, and what is the cell opposite the 19?
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34 − 20 = 14. 34 − 19 = 15.
9 Each term is the sum of the previous two: ?, ?, 7, 11, 18. What is the first term?
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Second term: 11 − 7 = 4. First term: 7 − 4 = 3. Check: 3, 4, 7, 11, 18 ✓.