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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 831 · 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.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 13 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 4 (d) 3
  4. 4.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 48 (c) 135 (d) 45
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 18 (d) 17
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  9. 9.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 134 (c) 142 (d) 124
  10. 10.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 85 (c) 86 (d) 76
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18
  13. 13.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 225 (c) 235 (d) 228
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  15. 15.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 138 (c) 130 (d) 129
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  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) 7 (b) 63 (c) 24 (d) 21
  18. 18.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) 438 (c) 540 (d) 549
  19. 19.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 556 (c) 555 (d) 442
  20. 20.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 579 (c) 464 (d) 588
  21. 21.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 360 (c) 361 (d) 312
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 7 (b) 19 (c) 17 (d) 18
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 19 (d) 20
  24. 24.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 229 (c) 228 (d) 219
  25. 25.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 618 (c) 484 (d) 609
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 17 (d) 18
  27. 27.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) 198 (c) 66 (d) 69
  28. 28.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 166 (c) 165 (d) 174
  29. 29.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 199 (c) 189 (d) 204
  30. 30.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) 36 (b) 33 (c) 99 (d) 11
  31. 31.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) 66 (b) 189 (c) 21 (d) 63
  32. 32.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 112 (c) 104 (d) 94
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 17 (d) 15
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 3 (d) 5
  35. 35.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) 19 (b) 57 (c) 60 (d) 171
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 16 (d) 17
  37. 37.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 381 (c) 390 (d) 332
  38. 38.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 468 (d) 469
  39. 39.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 156 (d) 138
  40. 40.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 157 (c) 148 (d) 158

Answer key

  1. 14
  2. 3
  3. 4
  4. 45
  5. 4
  6. 9
  7. 17
  8. 7
  9. 133
  10. 85
  11. 6
  12. 18
  13. 234
  14. 19
  15. 129
  16. 6
  17. 21
  18. 549
  19. 555
  20. 588
  21. 360
  22. 18
  23. 19
  24. 228
  25. 618
  26. 18
  27. 66
  28. 165
  29. 198
  30. 33
  31. 63
  32. 103
  33. 16
  34. 5
  35. 57
  36. 17
  37. 390
  38. 468
  39. 147
  40. 157

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