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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 775 · 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 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 543 (c) 534 (d) 434
  2. 2.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) 10 (b) 90 (c) 30 (d) 33
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  4. 4.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) 54 (b) 21 (c) 6 (d) 18
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 9 (c) 19 (d) 20
  6. 6.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) 66 (b) 22 (c) 198 (d) 69
  7. 7.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 430 (c) 358 (d) 420
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 18 (d) 19
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  10. 10.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 422 (c) 526 (d) 516
  11. 11.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 402 (c) 346 (d) 411
  12. 12.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) 54 (d) 153
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  16. 16.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) 24 (c) 75 (d) 72
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (d) 6
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 17 (d) 6
  19. 19.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 483 (c) 394 (d) 484
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  21. 21.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 288 (d) 279
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  23. 23.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 30 (c) 48 (d) 39
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
  26. 26.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 89 (c) 90 (d) 98
  27. 27.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 231 (c) 222 (d) 232
  28. 28.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) 516 (c) 517 (d) 416
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 17 (c) 6 (d) 16
  30. 30.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 468 (c) 384 (d) 459
  31. 31.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) 99 (c) 11 (d) 33
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  33. 33.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) 158 (d) 148
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  36. 36.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) 94 (c) 104 (d) 112
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  38. 38.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) 5 (b) 45 (c) 18 (d) 15
  39. 39.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 6

Answer key

  1. 543
  2. 30
  3. 2
  4. 18
  5. 19
  6. 66
  7. 429
  8. 18
  9. 17
  10. 525
  11. 411
  12. 51
  13. 5
  14. 19
  15. 8
  16. 72
  17. 17
  18. 17
  19. 483
  20. 7
  21. 288
  22. 6
  23. 39
  24. 5
  25. 5
  26. 89
  27. 231
  28. 516
  29. 17
  30. 468
  31. 33
  32. 8
  33. 157
  34. 9
  35. 20
  36. 103
  37. 3
  38. 15
  39. 81
  40. 5

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