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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 125 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 86 (c) 96 (d) 104
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 16 (d) 18
  3. 3.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 66 (c) 63 (d) 21
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  5. 5.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 267 (c) 276 (d) 256
  6. 6.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) 18 (c) 162 (d) 57
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 5 (b) 7 (c) 4 (d) 6
  8. 8.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 146 (c) 164 (d) 156
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 3 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 7 (b) 6 (c) 5 (d) 8
  12. 12.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) 23 (b) 69 (c) 207 (d) 72
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  14. 14.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) 117 (b) 39 (c) 42 (d) 13
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
  17. 17.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 279 (c) 288 (d) 264
  18. 18.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 118 (c) 100 (d) 110
  19. 19.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) 5 (c) 18 (d) 15
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 18 (d) 17
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 4 (d) 5
  22. 22.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 36 (c) 35 (d) 44
  23. 23.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 540 (c) 549 (d) 438
  24. 24.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) 57 (b) 60 (c) 171 (d) 19
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 8 (d) 20
  26. 26.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) 69 (c) 66 (d) 198
  27. 27.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 10 (c) 90 (d) 33
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  29. 29.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 52 (c) 61 (d) 62
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 7 (b) 5 (c) 6 (d) 8
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 6 (c) 4 (d) 5
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  33. 33.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) 72 (b) 27 (c) 24 (d) 8
  34. 34.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 81 (d) 30
  35. 35.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 74 (c) 84 (d) 83
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 13 (c) 12 (d) 7
  37. 37.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) 21 (b) 63 (c) 24 (d) 7
  38. 38.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 19 (d) 20
  40. 40.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 115 (c) 106 (d) 116

Answer key

  1. 95
  2. 17
  3. 63
  4. 5
  5. 276
  6. 54
  7. 6
  8. 155
  9. 4
  10. 2
  11. 7
  12. 69
  13. 3
  14. 39
  15. 8
  16. 17
  17. 288
  18. 109
  19. 15
  20. 18
  21. 5
  22. 35
  23. 549
  24. 57
  25. 19
  26. 66
  27. 30
  28. 9
  29. 61
  30. 7
  31. 5
  32. 15
  33. 24
  34. 27
  35. 83
  36. 12
  37. 21
  38. 60
  39. 20
  40. 115

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