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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 631 · 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 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 309 (c) 310 (d) 300
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 6 (b) 5 (c) 4 (d) 7
  3. 3.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) 162 (b) 57 (c) 54 (d) 18
  4. 4.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 624 (c) 633 (d) 494
  5. 5.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 510 (c) 520 (d) 418
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 18 (d) 17
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 8 (c) 7 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  9. 9.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) 469 (d) 468
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  12. 12.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 523 (d) 420
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 8 (c) 9 (d) 7
  14. 14.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 333 (c) 343 (d) 342
  15. 15.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
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  17. 17.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) 33 (b) 10 (c) 30 (d) 90
  18. 18.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 302 (c) 345 (d) 336
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  20. 20.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 345 (c) 308 (d) 354
  21. 21.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 198 (c) 199 (d) 204
  22. 22.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 52 (c) 34 (d) 43
  23. 23.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 262 (c) 286 (d) 276
  24. 24.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 44 (c) 54 (d) 53
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 6 (b) 4 (c) 5 (d) 7
  26. 26.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
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 19 (d) 18
  28. 28.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) 72 (c) 27 (d) 8
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 9 (b) 7 (c) 6 (d) 8
  33. 33.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) 453 (c) 374 (d) 444
  34. 34.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 137 (d) 138
  35. 35.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) 13 (b) 42 (c) 39 (d) 117
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  37. 37.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 276 (c) 277 (d) 267
  38. 38.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 487 (c) 396 (d) 486
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 6 (b) 7 (c) 5 (d) 8
  40. 40.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 79 (d) 88

Answer key

  1. 309
  2. 6
  3. 54
  4. 633
  5. 519
  6. 17
  7. 8
  8. 5
  9. 468
  10. 9
  11. 9
  12. 522
  13. 8
  14. 342
  15. 60
  16. 2
  17. 30
  18. 345
  19. 5
  20. 354
  21. 198
  22. 43
  23. 285
  24. 53
  25. 6
  26. 15
  27. 18
  28. 24
  29. 8
  30. 19
  31. 5
  32. 8
  33. 453
  34. 137
  35. 39
  36. 6
  37. 276
  38. 486
  39. 7
  40. 79

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