Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 660 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 17 (d) 15
2. 2.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 36 (c) 99 (d) 11
3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 4 (b) 5 (c) 2 (d) 3
5. 5.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 39 (c) 117 (d) 13
6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 12 (b) 14 (c) 15 (d) 9
7. 7.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
8. 8.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
9. 9.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 79 (d) 80
10. 10.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 27 (c) 72 (d) 8
11. 11.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 24 (d) 75
12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 17 (b) 16 (c) 5 (d) 15
13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 7 (b) 6 (c) 8 (d) 9
14. 14.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 21 (c) 54 (d) 18
15. 15.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 18 (c) 15 (d) 5
16. 16.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 126 (c) 117 (d) 118
17. 17.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 21 (c) 7 (d) 63
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 6 (b) 10 (c) 8 (d) 11
19. 19.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 621 (c) 492 (d) 630
20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
21. 21.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 153 (c) 51 (d) 17
22. 22.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 478 (d) 609
23. 23.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 8 (b) 9 (c) 6 (d) 7
25. 25.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 93 (d) 84
26. 26.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
27. 27.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
28. 28.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 57 (d) 18
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 4 (c) 12 (d) 14
31. 31.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 325 (c) 315 (d) 288
32. 32.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 207 (c) 23 (d) 72
33. 33.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 390 (c) 468 (d) 478
34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 7 (b) 5 (c) 6 (d) 8
35. 35.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 486 (c) 402 (d) 496
36. 36.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
37. 37.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 170 (c) 178 (d) 160
38. 38.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
39. 39.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 66 (c) 69 (d) 198
40. 40.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 19 (c) 171 (d) 57

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