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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 408 · 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 5 written when you write all the numbers from 1 to 53? (a) 10 (b) 5 (c) 9 (d) 7
  2. 2.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 258 (c) 267 (d) 250
  3. 3.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) 122 (d) 114
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 21 (d) 20
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 20 (c) 8 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  7. 7.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 235 (d) 234
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  9. 9.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) 57 (c) 171 (d) 60
  10. 10.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 106 (c) 96 (d) 105
  11. 11.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) 10 (b) 30 (c) 33 (d) 90
  12. 12.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 212 (c) 201 (d) 211
  13. 13.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 480 (d) 471
  14. 14.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) 180 (b) 20 (c) 60 (d) 63
  15. 15.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 107 (c) 98 (d) 116
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  18. 18.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 514 (c) 504 (d) 414
  19. 19.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 68 (c) 58 (d) 67
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  22. 22.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) 636 (c) 637 (d) 627
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 3 (b) 13 (c) 15 (d) 14
  25. 25.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) 18 (d) 15
  26. 26.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
  27. 27.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) 198 (b) 22 (c) 69 (d) 66
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 2 (d) 1
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 5 (c) 4 (d) 6
  32. 32.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 546 (c) 556 (d) 555
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 4 (d) 14
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 19 (d) 18
  35. 35.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 204 (c) 213 (d) 321
  36. 36.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 338 (d) 390
  37. 37.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 388 (c) 474 (d) 465
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 7 (b) 6 (c) 5 (d) 8

Answer key

  1. 9
  2. 267
  3. 113
  4. 20
  5. 19
  6. 7
  7. 234
  8. 4
  9. 57
  10. 105
  11. 30
  12. 210
  13. 480
  14. 60
  15. 107
  16. 3
  17. 6
  18. 513
  19. 67
  20. 4
  21. 5
  22. 636
  23. 3
  24. 14
  25. 15
  26. 54
  27. 66
  28. 8
  29. 6
  30. 3
  31. 6
  32. 555
  33. 15
  34. 19
  35. 213
  36. 399
  37. 474
  38. 5
  39. 2
  40. 7

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