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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 293 · 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 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 252 (c) 253 (d) 240
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 21 (b) 20 (c) 19 (d) 9
  6. 6.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 124 (c) 142 (d) 133
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  8. 8.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 82 (c) 73 (d) 64
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 18 (d) 16
  10. 10.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 94 (c) 103 (d) 112
  11. 11.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) 15 (d) 18
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 2 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 5 (b) 7 (c) 6 (d) 8
  16. 16.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) 27 (b) 9 (c) 30 (d) 81
  17. 17.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 122 (c) 112 (d) 121
  18. 18.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 56 (c) 55 (d) 64
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 5 (b) 3 (c) 4 (d) 2
  20. 20.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 118 (c) 128 (d) 136
  21. 21.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 532 (b) 531 (c) 426 (d) 522
  22. 22.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) 12 (b) 36 (c) 108 (d) 39
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 19 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 6 (b) 3 (c) 4 (d) 5
  26. 26.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) 6 (c) 21 (d) 54
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 6 (d) 15
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 4 (d) 5
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  31. 31.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) 66 (b) 63 (c) 21 (d) 189
  32. 32.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 258 (c) 259 (d) 249
  33. 33.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 77 (c) 68 (d) 78
  34. 34.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) 19 (b) 171 (c) 60 (d) 57
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  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) 22 (b) 69 (c) 66 (d) 198
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 7 (b) 6 (c) 8 (d) 5
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 17 (b) 19 (c) 18 (d) 8
  39. 39.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) 30 (c) 90 (d) 10
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 4 (d) 3

Answer key

  1. 252
  2. 2
  3. 7
  4. 4
  5. 20
  6. 133
  7. 2
  8. 73
  9. 17
  10. 103
  11. 15
  12. 4
  13. 5
  14. 15
  15. 7
  16. 27
  17. 121
  18. 55
  19. 4
  20. 127
  21. 531
  22. 36
  23. 19
  24. 7
  25. 5
  26. 18
  27. 9
  28. 16
  29. 5
  30. 3
  31. 63
  32. 258
  33. 77
  34. 57
  35. 3
  36. 66
  37. 7
  38. 18
  39. 30
  40. 4

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