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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 6 · 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 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  2. 2.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
  3. 3.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 154 (c) 162 (d) 153
  4. 4.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 188 (c) 179 (d) 170
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  6. 6.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 466 (c) 382 (d) 465
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  8. 8.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) 207 (c) 72 (d) 69
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 19 (d) 17
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  11. 11.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) 51 (c) 153 (d) 17
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  13. 13.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 292 (c) 330 (d) 331
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
  15. 15.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  17. 17.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 59 (c) 60 (d) 68
  18. 18.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) 48 (b) 16 (c) 51 (d) 144
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 17 (c) 16 (d) 15
  20. 20.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) 117 (c) 42 (d) 13
  21. 21.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 230 (c) 237 (d) 228
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 4 (d) 1
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 7 (d) 18
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 18 (d) 6
  26. 26.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) 63 (b) 7 (c) 21 (d) 24
  27. 27.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 124 (c) 114 (d) 123
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 1 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  30. 30.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 279 (c) 280 (d) 258
  31. 31.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 628 (c) 627 (d) 618
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 19 (d) 18
  33. 33.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 111 (c) 112 (d) 102
  34. 34.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
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 10 (b) 8 (c) 7 (d) 9
  38. 38.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 16 (d) 15
  40. 40.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 214 (d) 204

Answer key

  1. 18
  2. 57
  3. 153
  4. 179
  5. 4
  6. 465
  7. 2
  8. 69
  9. 18
  10. 8
  11. 51
  12. 4
  13. 330
  14. 3
  15. 117
  16. 7
  17. 59
  18. 48
  19. 16
  20. 39
  21. 237
  22. 9
  23. 3
  24. 18
  25. 17
  26. 21
  27. 123
  28. 3
  29. 5
  30. 279
  31. 627
  32. 19
  33. 111
  34. 54
  35. 7
  36. 4
  37. 9
  38. 6
  39. 15
  40. 213

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