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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 651 · 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 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 7 (c) 6 (d) 5
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 18 (d) 19
  3. 3.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 130 (c) 112 (d) 121
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  6. 6.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) 63 (b) 66 (c) 21 (d) 189
  7. 7.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) 104 (c) 103 (d) 94
  8. 8.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 478 (c) 600 (d) 610
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  11. 11.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 262 (c) 285 (d) 286
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 10 (c) 13 (d) 7
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 3 (d) 6
  14. 14.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) 15 (c) 45 (d) 48
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 9 (b) 6 (c) 11 (d) 12
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 19 (d) 8
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  21. 21.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 130 (c) 140 (d) 139
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  23. 23.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
  24. 24.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 171 (d) 60
  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.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 21
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
  29. 29.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) 23 (b) 72 (c) 207 (d) 69
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  31. 31.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 45 (c) 42 (d) 14
  32. 32.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) 45 (b) 5 (c) 18 (d) 15
  33. 33.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 41 (c) 32 (d) 50
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 7 (c) 4 (d) 5
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  37. 37.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 166 (c) 165 (d) 174
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14
  39. 39.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) 12 (d) 39
  40. 40.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 167 (d) 168

Answer key

  1. 7
  2. 19
  3. 121
  4. 18
  5. 5
  6. 63
  7. 103
  8. 609
  9. 14
  10. 5
  11. 285
  12. 12
  13. 5
  14. 45
  15. 8
  16. 4
  17. 4
  18. 11
  19. 18
  20. 4
  21. 139
  22. 6
  23. 18
  24. 57
  25. 54
  26. 2
  27. 20
  28. 15
  29. 69
  30. 2
  31. 42
  32. 15
  33. 41
  34. 17
  35. 7
  36. 3
  37. 165
  38. 14
  39. 36
  40. 167

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