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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 558 · 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 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 336 (c) 327 (d) 296
  2. 2.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 39 (c) 40 (d) 48
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 4 (d) 3
  4. 4.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) 117 (c) 118 (d) 126
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 5 (c) 15 (d) 16
  6. 6.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) 90 (b) 30 (c) 33 (d) 10
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 7 (d) 4
  8. 8.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
  9. 9.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 374 (c) 444 (d) 453
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 18 (d) 17
  11. 11.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 325 (c) 324 (d) 315
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 15 (d) 17
  14. 14.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 178 (c) 196 (d) 188
  15. 15.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 619 (c) 484 (d) 618
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 14 (c) 13 (d) 4
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 6 (b) 5 (c) 7 (d) 4
  19. 19.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 316 (c) 306 (d) 315
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 5 (d) 6
  21. 21.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 202 (c) 201 (d) 192
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  23. 23.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 154 (c) 164 (d) 172
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 5 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17
  29. 29.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 361 (c) 360 (d) 351
  30. 30.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 204 (c) 321 (d) 213
  31. 31.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 476 (c) 597 (d) 607
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
  33. 33.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 98 (c) 107 (d) 116
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 12 (b) 8 (c) 11 (d) 9
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 6 (d) 18
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 16 (d) 17
  37. 37.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) 48 (b) 135 (c) 15 (d) 45
  38. 38.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 41 (d) 32
  39. 39.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 381 (c) 326 (d) 372
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14

Answer key

  1. 336
  2. 39
  3. 5
  4. 117
  5. 15
  6. 30
  7. 6
  8. 54
  9. 453
  10. 18
  11. 324
  12. 5
  13. 16
  14. 187
  15. 618
  16. 16
  17. 13
  18. 6
  19. 315
  20. 5
  21. 201
  22. 5
  23. 163
  24. 5
  25. 8
  26. 7
  27. 20
  28. 17
  29. 360
  30. 213
  31. 606
  32. 3
  33. 107
  34. 11
  35. 17
  36. 16
  37. 45
  38. 41
  39. 381
  40. 14

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