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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 536 · 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 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 15 (d) 16
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 7 (d) 17
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  4. 4.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) 15 (b) 18 (c) 5 (d) 45
  5. 5.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 139 (c) 148 (d) 130
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 20 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 18
  12. 12.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 252 (d) 253
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 17 (d) 6
  14. 14.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 216 (d) 217
  15. 15.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 142 (c) 124 (d) 133
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 6 (d) 4
  17. 17.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 574 (c) 454 (d) 564
  18. 18.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 450 (c) 568 (d) 567
  19. 19.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 247 (c) 237 (d) 246
  20. 20.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 180 (c) 198 (d) 190
  21. 21.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 589 (c) 579 (d) 464
  22. 22.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) 12 (b) 108 (c) 36 (d) 39
  23. 23.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 268 (c) 250 (d) 267
  24. 24.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) 60 (c) 20 (d) 63
  25. 25.The numbers 11 to 19 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) 15 (c) 135 (d) 45
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 16 (d) 17
  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) 69 (b) 66 (c) 198 (d) 22
  28. 28.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 39 (c) 13 (d) 117
  29. 29.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) 114 (c) 122 (d) 104
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  31. 31.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 622 (c) 621 (d) 486
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 7 (c) 8 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  35. 35.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 406 (c) 342 (d) 396
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 8 (d) 18
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 14 (d) 4
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  40. 40.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 345 (c) 302 (d) 346

Answer key

  1. 15
  2. 17
  3. 3
  4. 15
  5. 139
  6. 4
  7. 19
  8. 5
  9. 7
  10. 18
  11. 19
  12. 252
  13. 17
  14. 216
  15. 133
  16. 6
  17. 573
  18. 567
  19. 246
  20. 189
  21. 588
  22. 36
  23. 267
  24. 60
  25. 45
  26. 16
  27. 66
  28. 39
  29. 113
  30. 8
  31. 621
  32. 20
  33. 7
  34. 8
  35. 405
  36. 19
  37. 14
  38. 17
  39. 5
  40. 345

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