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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 730 · 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 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 74 (d) 84
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 6 (b) 9 (c) 7 (d) 8
  5. 5.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 154 (c) 136 (d) 145
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 19 (d) 18
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  9. 9.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 176 (c) 194 (d) 186
  10. 10.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 216 (d) 72
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 2 (d) 3
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 16 (d) 15
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 13 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  15. 15.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 113 (c) 122 (d) 114
  16. 16.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) 51 (b) 144 (c) 16 (d) 48
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 18 (d) 17
  18. 18.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 204 (c) 189 (d) 199
  19. 19.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) 57 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  21. 21.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 85 (d) 76
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 5 (c) 3 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  25. 25.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) 6 (b) 54 (c) 21 (d) 18
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 19 (c) 7 (d) 17
  27. 27.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) 33 (b) 90 (c) 30 (d) 10
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 6 (c) 4 (d) 5
  30. 30.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) 54 (b) 153 (c) 17 (d) 51
  31. 31.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) 24 (c) 21 (d) 63
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  33. 33.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) 90 (c) 81 (d) 82
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  35. 35.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 219 (c) 224 (d) 229
  36. 36.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) 66 (b) 198 (c) 69 (d) 22
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 14 (d) 15
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 8 (c) 15 (d) 13
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 17 (d) 19
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7

Answer key

  1. 83
  2. 6
  3. 6
  4. 8
  5. 145
  6. 19
  7. 24
  8. 5
  9. 185
  10. 72
  11. 4
  12. 15
  13. 14
  14. 2
  15. 113
  16. 48
  17. 18
  18. 198
  19. 54
  20. 5
  21. 85
  22. 14
  23. 4
  24. 4
  25. 18
  26. 18
  27. 30
  28. 8
  29. 5
  30. 51
  31. 21
  32. 17
  33. 81
  34. 9
  35. 228
  36. 66
  37. 15
  38. 15
  39. 18
  40. 18

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