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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 644 · 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 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 120 (c) 112 (d) 111
  2. 2.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) 27 (c) 72 (d) 24
  3. 3.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 487 (c) 396 (d) 486
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  6. 6.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) 12 (c) 36 (d) 39
  7. 7.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 114 (c) 96 (d) 106
  8. 8.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 627 (c) 618 (d) 490
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  11. 11.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 637 (c) 627 (d) 636
  12. 12.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 529 (c) 424 (d) 528
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  15. 15.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) 51 (c) 144 (d) 16
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 5 (d) 3
  17. 17.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 450 (c) 451 (d) 372
  18. 18.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) 30 (b) 10 (c) 33 (d) 90
  19. 19.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 276 (c) 277 (d) 267
  20. 20.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 432 (d) 541
  21. 21.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) 153 (b) 17 (c) 51 (d) 54
  22. 22.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) 45 (b) 126 (c) 42 (d) 14
  23. 23.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 176 (c) 166 (d) 184
  24. 24.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 474 (d) 394
  25. 25.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 70 (c) 80 (d) 88
  26. 26.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 140 (c) 149 (d) 150
  27. 27.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 447 (c) 370 (d) 438
  28. 28.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) 69 (c) 207 (d) 72
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 12 (c) 9 (d) 11
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 6 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  32. 32.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 252 (c) 271 (d) 270
  33. 33.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 228 (c) 219 (d) 229
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 17 (d) 16
  35. 35.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) 76 (c) 85 (d) 94
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 14 (d) 4
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 4 (d) 5
  38. 38.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
  39. 39.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) 24 (b) 75 (c) 216 (d) 72
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

  1. 111
  2. 24
  3. 486
  4. 4
  5. 9
  6. 36
  7. 105
  8. 627
  9. 4
  10. 9
  11. 636
  12. 528
  13. 19
  14. 3
  15. 48
  16. 4
  17. 450
  18. 30
  19. 276
  20. 540
  21. 51
  22. 42
  23. 175
  24. 483
  25. 79
  26. 149
  27. 447
  28. 69
  29. 11
  30. 17
  31. 8
  32. 270
  33. 228
  34. 17
  35. 85
  36. 14
  37. 5
  38. 103
  39. 72
  40. 3

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