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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 251 · 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 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 597 (c) 470 (d) 598
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  4. 4.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 294 (c) 334 (d) 333
  5. 5.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) 21 (c) 54 (d) 6
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 11 (c) 3 (d) 10
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  9. 9.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 118 (c) 126 (d) 108
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 5 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 2 (b) 5 (c) 3 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  15. 15.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) 27 (c) 81 (d) 9
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 13 (d) 14
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 9 (c) 3 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  19. 19.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) 7 (c) 21 (d) 63
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  21. 21.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 561 (c) 570 (d) 452
  22. 22.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) 16 (b) 48 (c) 51 (d) 144
  23. 23.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 380 (c) 463 (d) 453
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  25. 25.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) 39 (b) 108 (c) 12 (d) 36
  26. 26.The numbers 17 to 25 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) 189 (c) 63 (d) 66
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  28. 28.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) 11 (c) 33 (d) 99
  29. 29.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 140 (c) 139 (d) 148
  30. 30.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) 256 (c) 242 (d) 255
  31. 31.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 54 (c) 44 (d) 62
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 21 (d) 20
  33. 33.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 94 (c) 103 (d) 104
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
  35. 35.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) 22 (d) 69
  36. 36.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) 51 (d) 54
  37. 37.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 573 (c) 454 (d) 564
  38. 38.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 93 (c) 94 (d) 84
  39. 39.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
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 19 (d) 18

Answer key

  1. 597
  2. 20
  3. 9
  4. 333
  5. 18
  6. 11
  7. 6
  8. 8
  9. 117
  10. 18
  11. 5
  12. 9
  13. 4
  14. 7
  15. 27
  16. 14
  17. 9
  18. 6
  19. 21
  20. 2
  21. 570
  22. 48
  23. 462
  24. 3
  25. 36
  26. 63
  27. 20
  28. 33
  29. 139
  30. 255
  31. 53
  32. 20
  33. 103
  34. 14
  35. 66
  36. 51
  37. 573
  38. 93
  39. 5
  40. 19

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