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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 371 · 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 5 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 19 (d) 18
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  3. 3.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 217 (c) 324 (d) 216
  4. 4.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) 57 (c) 54 (d) 18
  5. 5.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 82 (c) 81 (d) 90
  6. 6.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) 42 (c) 117 (d) 13
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 7 (d) 16
  9. 9.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 104 (c) 114 (d) 122
  10. 10.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 520 (c) 519 (d) 510
  11. 11.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 252 (c) 253 (d) 243
  12. 12.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) 60 (c) 20 (d) 180
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 4 (d) 6
  14. 14.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 82 (c) 92 (d) 91
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 17 (d) 18
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 16 (d) 18
  17. 17.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) 108 (b) 36 (c) 39 (d) 12
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  21. 21.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 132 (c) 142 (d) 141
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  24. 24.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 86 (c) 68 (d) 77
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 19 (d) 20
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  27. 27.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) 72 (c) 27 (d) 24
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 5 (c) 6 (d) 4
  29. 29.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 630 (c) 631 (d) 621
  30. 30.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 52 (c) 51 (d) 42
  31. 31.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) 153 (b) 17 (c) 54 (d) 51
  32. 32.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) 9 (b) 27 (c) 81 (d) 30
  33. 33.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 391 (d) 381
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 17 (d) 18
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 11 (c) 12 (d) 13
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 7 (c) 8 (d) 9

Answer key

  1. 18
  2. 2
  3. 216
  4. 54
  5. 81
  6. 39
  7. 6
  8. 17
  9. 113
  10. 519
  11. 252
  12. 60
  13. 5
  14. 91
  15. 18
  16. 17
  17. 36
  18. 3
  19. 5
  20. 5
  21. 141
  22. 6
  23. 8
  24. 77
  25. 19
  26. 7
  27. 24
  28. 5
  29. 630
  30. 51
  31. 51
  32. 27
  33. 390
  34. 9
  35. 8
  36. 18
  37. 18
  38. 12
  39. 16
  40. 8

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