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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 386 · 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 1 written when you write all the numbers from 1 to 93? (a) 21 (b) 19 (c) 9 (d) 20
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  3. 3.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) 48 (c) 15 (d) 45
  4. 4.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) 144 (b) 16 (c) 51 (d) 48
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  7. 7.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 92 (c) 83 (d) 74
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 3 (d) 4
  12. 12.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 154 (c) 136 (d) 145
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 5 (b) 6 (c) 7 (d) 4
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 3 (d) 4
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  16. 16.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 609 (d) 478
  17. 17.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
  18. 18.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) 108 (d) 39
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  21. 21.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 444 (c) 558 (d) 549
  22. 22.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) 27 (b) 9 (c) 30 (d) 81
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
  24. 24.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) 105 (c) 114 (d) 96
  25. 25.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) 18 (c) 57 (d) 54
  26. 26.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 460 (d) 582
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 18 (d) 17
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 19 (d) 9
  29. 29.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 516 (c) 525 (d) 422
  30. 30.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 466 (c) 582 (d) 592
  31. 31.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) 8 (b) 27 (c) 72 (d) 24
  32. 32.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) 53 (c) 44 (d) 54
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  34. 34.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 158 (c) 166 (d) 157
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 17 (d) 19
  38. 38.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 208 (c) 204 (d) 205
  39. 39.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 522 (c) 420 (d) 513
  40. 40.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) 48 (c) 39 (d) 30

Answer key

  1. 20
  2. 9
  3. 45
  4. 48
  5. 6
  6. 3
  7. 83
  8. 15
  9. 8
  10. 4
  11. 3
  12. 145
  13. 6
  14. 5
  15. 4
  16. 609
  17. 15
  18. 36
  19. 7
  20. 5
  21. 558
  22. 27
  23. 3
  24. 105
  25. 54
  26. 582
  27. 18
  28. 20
  29. 525
  30. 591
  31. 24
  32. 53
  33. 3
  34. 157
  35. 20
  36. 7
  37. 18
  38. 204
  39. 522
  40. 39

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