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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 959 · 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 times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 20 (b) 18 (c) 9 (d) 19
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  4. 4.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 495 (c) 408 (d) 505
  5. 5.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 348 (c) 414 (d) 415
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20
  7. 7.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) 39 (b) 117 (c) 42 (d) 13
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  9. 9.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 97 (c) 106 (d) 88
  10. 10.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) 27 (b) 8 (c) 72 (d) 24
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 17
  12. 12.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 114 (d) 105
  13. 13.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) 12 (c) 39 (d) 108
  14. 14.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 270 (d) 298
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 7 (b) 6 (c) 9 (d) 8
  17. 17.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 549 (c) 444 (d) 559
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  19. 19.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 30 (d) 27
  20. 20.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) 69 (c) 207 (d) 72
  21. 21.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 340 (c) 339 (d) 298
  22. 22.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) 5 (d) 15
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 13
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  26. 26.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 72 (d) 71
  27. 27.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) 11 (b) 99 (c) 36 (d) 33
  28. 28.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 60 (c) 59 (d) 68
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 5 (d) 3
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 4 (c) 3 (d) 5
  31. 31.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 333 (c) 324 (d) 294
  32. 32.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 478 (d) 477
  33. 33.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 42 (c) 126 (d) 45
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  35. 35.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 636 (d) 496
  36. 36.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) 7 (b) 21 (c) 63 (d) 24
  37. 37.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) 57 (b) 162 (c) 18 (d) 54
  38. 38.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 80 (c) 98 (d) 90
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  40. 40.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) 45 (b) 48 (c) 135 (d) 15

Answer key

  1. 4
  2. 19
  3. 6
  4. 504
  5. 414
  6. 19
  7. 39
  8. 3
  9. 97
  10. 24
  11. 16
  12. 105
  13. 36
  14. 297
  15. 6
  16. 8
  17. 558
  18. 17
  19. 27
  20. 69
  21. 339
  22. 15
  23. 14
  24. 3
  25. 4
  26. 71
  27. 33
  28. 59
  29. 4
  30. 5
  31. 333
  32. 477
  33. 42
  34. 9
  35. 636
  36. 21
  37. 54
  38. 89
  39. 2
  40. 45

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