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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 919 · 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 7 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 3 (d) 5
  2. 2.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) 370 (c) 447 (d) 438
  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) 18 (b) 54 (c) 6 (d) 21
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 3 (d) 15
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  7. 7.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) 72 (b) 27 (c) 24 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  9. 9.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 134 (d) 144
  10. 10.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 316 (c) 315 (d) 282
  11. 11.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 390 (c) 391 (d) 381
  12. 12.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 558 (c) 568 (d) 567
  13. 13.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) 96 (c) 106 (d) 105
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 15 (c) 9 (d) 13
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 6 (b) 15 (c) 13 (d) 14
  16. 16.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) 226 (c) 216 (d) 225
  17. 17.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 146 (c) 128 (d) 137
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  19. 19.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 74 (c) 64 (d) 82
  20. 20.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) 67 (c) 58 (d) 68
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 17 (b) 18 (c) 16 (d) 7
  22. 22.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 354 (c) 364 (d) 363
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 5 (d) 3
  26. 26.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 433 (c) 360 (d) 423
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  28. 28.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) 18 (b) 162 (c) 57 (d) 54
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  30. 30.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) 72 (b) 24 (c) 216 (d) 75
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  36. 36.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 28 (c) 37 (d) 38
  37. 37.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
  38. 38.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 372 (c) 381 (d) 382
  39. 39.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 280 (d) 312
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 4 (c) 14 (d) 16

Answer key

  1. 4
  2. 447
  3. 18
  4. 20
  5. 14
  6. 4
  7. 24
  8. 9
  9. 143
  10. 315
  11. 390
  12. 567
  13. 105
  14. 15
  15. 14
  16. 225
  17. 137
  18. 7
  19. 73
  20. 67
  21. 17
  22. 363
  23. 2
  24. 3
  25. 5
  26. 432
  27. 9
  28. 54
  29. 4
  30. 72
  31. 8
  32. 6
  33. 20
  34. 2
  35. 5
  36. 37
  37. 36
  38. 381
  39. 312
  40. 15

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