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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 33 · 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 two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  3. 3.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 511 (c) 412 (d) 501
  4. 4.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 592 (c) 591 (d) 582
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 6 (b) 7 (c) 4 (d) 5
  6. 6.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) 116 (d) 106
  7. 7.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
  8. 8.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 549 (c) 558 (d) 559
  9. 9.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) 17 (b) 51 (c) 153 (d) 54
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  11. 11.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 315 (c) 306 (d) 282
  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) 72 (c) 69 (d) 207
  13. 13.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 94 (d) 102
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  16. 16.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
  17. 17.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) 8 (d) 27
  18. 18.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 628 (c) 627 (d) 490
  19. 19.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 433 (c) 360 (d) 432
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 2 (d) 3
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  22. 22.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 66 (c) 65 (d) 74
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 17 (d) 18
  27. 27.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 397 (c) 336 (d) 396
  28. 28.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 357 (c) 348 (d) 358
  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) 351 (b) 361 (c) 312 (d) 360
  30. 30.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 62 (c) 70 (d) 61
  31. 31.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) 10 (c) 33 (d) 30
  32. 32.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 408 (c) 418 (d) 350
  33. 33.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) 75 (c) 24 (d) 72
  34. 34.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 64 (c) 63 (d) 54
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 3 (b) 4 (c) 5 (d) 6
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 19 (d) 17
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 5 (c) 4 (d) 6

Answer key

  1. 3
  2. 4
  3. 510
  4. 591
  5. 6
  6. 115
  7. 381
  8. 558
  9. 51
  10. 2
  11. 315
  12. 69
  13. 93
  14. 19
  15. 5
  16. 45
  17. 24
  18. 627
  19. 432
  20. 3
  21. 18
  22. 65
  23. 3
  24. 7
  25. 7
  26. 18
  27. 396
  28. 357
  29. 360
  30. 61
  31. 30
  32. 417
  33. 72
  34. 63
  35. 5
  36. 18
  37. 9
  38. 5
  39. 6
  40. 6

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