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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 529 · 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 2 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 8 (d) 20
  2. 2.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 98 (c) 108 (d) 116
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 10 (c) 8 (d) 9
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 21 (d) 19
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 5 (b) 7 (c) 4 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 20 (d) 21
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 15 (d) 13
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 9 (c) 8 (d) 7
  13. 13.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) 54 (b) 21 (c) 6 (d) 18
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 18 (d) 19
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 17 (c) 18 (d) 9
  16. 16.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) 24 (d) 27
  17. 17.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 356 (d) 426
  18. 18.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) 69 (b) 23 (c) 207 (d) 72
  19. 19.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) 15 (b) 5 (c) 45 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  21. 21.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 38 (c) 47 (d) 56
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  23. 23.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
  24. 24.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 76 (c) 66 (d) 84
  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) 54 (c) 18 (d) 57
  26. 26.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 53 (c) 54 (d) 62
  27. 27.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 283 (c) 282 (d) 273
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 9 (d) 18
  29. 29.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 429 (c) 430 (d) 420
  30. 30.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 18 (d) 16
  32. 32.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 86 (d) 96
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 14 (d) 15
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 15 (d) 13
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 18 (d) 17
  36. 36.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 30 (d) 33
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 15 (c) 14 (d) 3
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 15 (d) 5
  39. 39.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) 51 (d) 54
  40. 40.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 99 (c) 90 (d) 100

Answer key

  1. 19
  2. 107
  3. 16
  4. 9
  5. 20
  6. 6
  7. 4
  8. 7
  9. 6
  10. 20
  11. 14
  12. 8
  13. 18
  14. 19
  15. 17
  16. 24
  17. 426
  18. 69
  19. 15
  20. 3
  21. 47
  22. 4
  23. 77
  24. 75
  25. 54
  26. 53
  27. 282
  28. 19
  29. 429
  30. 151
  31. 17
  32. 95
  33. 15
  34. 14
  35. 17
  36. 30
  37. 14
  38. 16
  39. 51
  40. 99

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