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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 890 · 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 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 88 (c) 87 (d) 96
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 14 (c) 15 (d) 13
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 5 (d) 4
  4. 4.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 264 (c) 265 (d) 255
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
  7. 7.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 357 (c) 358 (d) 310
  8. 8.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) 72 (c) 24 (d) 216
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 15 (d) 4
  10. 10.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 429 (c) 439 (d) 364
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 3 (c) 14 (d) 15
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 8 (c) 7 (d) 5
  16. 16.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 330 (c) 339 (d) 340
  17. 17.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 363 (c) 354 (d) 314
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 19 (d) 9
  19. 19.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 280 (c) 312 (d) 303
  20. 20.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 264 (c) 289 (d) 288
  21. 21.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 54 (c) 72 (d) 63
  22. 22.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) 112 (c) 102 (d) 111
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 18 (d) 19
  24. 24.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 216 (c) 226 (d) 225
  25. 25.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) 9 (b) 81 (c) 30 (d) 27
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 12 (b) 10 (c) 4 (d) 11
  27. 27.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) 54 (c) 53 (d) 62
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  29. 29.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  30. 30.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 579 (c) 580 (d) 458
  31. 31.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  32. 32.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 444 (c) 368 (d) 445
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  35. 35.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) 60 (b) 19 (c) 57 (d) 171
  36. 36.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) 207 (b) 72 (c) 23 (d) 69
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 1 (d) 2
  38. 38.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 104 (c) 114 (d) 122
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  40. 40.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) 54 (b) 57 (c) 162 (d) 18

Answer key

  1. 87
  2. 14
  3. 5
  4. 264
  5. 3
  6. 16
  7. 357
  8. 72
  9. 15
  10. 438
  11. 3
  12. 4
  13. 5
  14. 14
  15. 7
  16. 339
  17. 363
  18. 19
  19. 312
  20. 288
  21. 63
  22. 111
  23. 18
  24. 225
  25. 27
  26. 11
  27. 53
  28. 2
  29. 8
  30. 579
  31. 9
  32. 444
  33. 5
  34. 6
  35. 57
  36. 69
  37. 3
  38. 113
  39. 6
  40. 54

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