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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 13 · 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 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 564 (c) 573 (d) 574
  2. 2.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 242 (c) 256 (d) 255
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  7. 7.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) 135 (b) 15 (c) 45 (d) 48
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 3 (b) 4 (c) 6 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 5 (b) 6 (c) 4 (d) 3
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 5 (d) 3
  13. 13.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 294 (c) 285 (d) 295
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 17 (d) 8
  15. 15.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 148 (c) 130 (d) 139
  16. 16.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 619 (c) 484 (d) 609
  17. 17.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 210 (c) 218 (d) 220
  18. 18.The numbers 2 to 10 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) 54 (c) 18 (d) 6
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 4 (b) 6 (c) 5 (d) 3
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 16 (b) 17 (c) 6 (d) 15
  21. 21.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 516 (d) 517
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 7 (b) 9 (c) 6 (d) 8
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 4 (d) 3
  24. 24.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
  25. 25.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 234 (c) 228 (d) 225
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  27. 27.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) 180 (c) 60 (d) 20
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  29. 29.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 339 (c) 348 (d) 349
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 20 (d) 9
  31. 31.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) 24 (b) 21 (c) 63 (d) 7
  32. 32.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) 15 (d) 18
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  36. 36.The numbers 12 to 20 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) 51 (c) 144 (d) 16
  37. 37.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) 153 (c) 54 (d) 51
  38. 38.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 535 (c) 428 (d) 534
  39. 39.The numbers 8 to 16 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) 39 (c) 12 (d) 108
  40. 40.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 423 (c) 433 (d) 432

Answer key

  1. 573
  2. 255
  3. 2
  4. 18
  5. 17
  6. 4
  7. 45
  8. 6
  9. 5
  10. 9
  11. 5
  12. 4
  13. 294
  14. 18
  15. 139
  16. 618
  17. 219
  18. 18
  19. 5
  20. 16
  21. 516
  22. 8
  23. 4
  24. 30
  25. 234
  26. 16
  27. 60
  28. 3
  29. 348
  30. 20
  31. 21
  32. 15
  33. 20
  34. 15
  35. 9
  36. 48
  37. 51
  38. 534
  39. 36
  40. 432

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