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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 63 · 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 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 5 (d) 4
  2. 2.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 183 (d) 200
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 16 (c) 5 (d) 15
  4. 4.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 86 (c) 78 (d) 77
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  7. 7.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) 198 (b) 66 (c) 69 (d) 22
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  9. 9.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) 63 (c) 21 (d) 24
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  13. 13.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 564 (c) 448 (d) 555
  14. 14.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 72 (c) 82 (d) 81
  15. 15.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 158 (c) 167 (d) 176
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 18 (d) 20
  17. 17.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 102 (c) 84 (d) 93
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 15 (d) 5
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 18 (d) 17
  21. 21.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) 18 (b) 6 (c) 21 (d) 54
  22. 22.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 121 (c) 122 (d) 130
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  24. 24.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 456 (c) 466 (d) 465
  25. 25.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 50 (d) 49
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 20 (d) 19
  27. 27.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) 30 (b) 81 (c) 27 (d) 9
  28. 28.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 314 (c) 364 (d) 363
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 12 (c) 7 (d) 14
  31. 31.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) 48 (b) 135 (c) 45 (d) 15
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  33. 33.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) 207 (b) 69 (c) 72 (d) 23
  34. 34.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 446 (c) 562 (d) 561
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 6 (c) 4 (d) 7
  36. 36.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 135 (c) 126 (d) 144
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 1 (d) 4
  38. 38.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) 20 (c) 180 (d) 60
  39. 39.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 69 (c) 70 (d) 60
  40. 40.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) 12 (b) 108 (c) 36 (d) 39

Answer key

  1. 5
  2. 192
  3. 16
  4. 77
  5. 2
  6. 9
  7. 66
  8. 9
  9. 21
  10. 19
  11. 6
  12. 2
  13. 564
  14. 81
  15. 167
  16. 19
  17. 93
  18. 16
  19. 16
  20. 18
  21. 18
  22. 121
  23. 3
  24. 465
  25. 49
  26. 19
  27. 27
  28. 363
  29. 18
  30. 14
  31. 45
  32. 20
  33. 69
  34. 561
  35. 6
  36. 135
  37. 3
  38. 60
  39. 69
  40. 36

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