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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 171 · 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 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 453 (c) 444 (d) 374
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  3. 3.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) 18 (c) 21 (d) 54
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 3 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  6. 6.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 417 (d) 350
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 6 (b) 9 (c) 7 (d) 8
  8. 8.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 241 (c) 231 (d) 240
  9. 9.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 534 (c) 544 (d) 434
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 17
  11. 11.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 529 (c) 519 (d) 528
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 12 (c) 13 (d) 3
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  14. 14.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 388 (c) 465 (d) 475
  15. 15.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 414 (c) 423 (d) 354
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 18 (c) 7 (d) 17
  17. 17.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 387 (c) 336 (d) 397
  18. 18.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 71 (d) 62
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 7 (d) 6
  20. 20.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 84 (d) 83
  21. 21.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) 106 (c) 96 (d) 114
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 3 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  24. 24.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 174 (c) 165 (d) 156
  25. 25.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
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  27. 27.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 308 (c) 345 (d) 354
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  29. 29.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) 24 (d) 72
  30. 30.The numbers 16 to 24 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) 180 (c) 20 (d) 63
  31. 31.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 145 (c) 146 (d) 136
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 17 (d) 5
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  34. 34.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) 21 (c) 24 (d) 63
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 1 (d) 4
  36. 36.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) 30 (c) 27 (d) 81
  37. 37.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) 33 (c) 10 (d) 90
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  39. 39.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) 36 (b) 108 (c) 12 (d) 39
  40. 40.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) 16 (b) 48 (c) 51 (d) 144

Answer key

  1. 453
  2. 7
  3. 18
  4. 4
  5. 2
  6. 417
  7. 8
  8. 240
  9. 543
  10. 18
  11. 528
  12. 13
  13. 2
  14. 474
  15. 423
  16. 18
  17. 396
  18. 71
  19. 7
  20. 83
  21. 105
  22. 4
  23. 9
  24. 165
  25. 18
  26. 4
  27. 354
  28. 3
  29. 24
  30. 60
  31. 145
  32. 16
  33. 20
  34. 21
  35. 3
  36. 27
  37. 30
  38. 5
  39. 36
  40. 48

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