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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 504 · 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 two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 16 (d) 5
  3. 3.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 204 (c) 189 (d) 199
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 17 (d) 19
  5. 5.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
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 18 (d) 17
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 20 (d) 19
  9. 9.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
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 11 (b) 9 (c) 4 (d) 10
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 18
  13. 13.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 609 (c) 610 (d) 478
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  15. 15.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) 363 (c) 354 (d) 364
  16. 16.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 109 (c) 110 (d) 118
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 7 (d) 17
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 5 (d) 6
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 5 (b) 14 (c) 16 (d) 15
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 6 (c) 9 (d) 11
  23. 23.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 58 (c) 49 (d) 50
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  26. 26.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 218 (c) 210 (d) 219
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 14 (c) 13 (d) 15
  28. 28.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) 51 (c) 54 (d) 17
  29. 29.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 316 (c) 282 (d) 306
  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) 75 (c) 24 (d) 216
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 5 (c) 7 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  34. 34.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 522 (c) 426 (d) 532
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  37. 37.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 387 (c) 330 (d) 388
  38. 38.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) 30 (b) 81 (c) 9 (d) 27
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 17 (d) 6
  40. 40.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) 33 (b) 10 (c) 30 (d) 90

Answer key

  1. 6
  2. 16
  3. 198
  4. 18
  5. 15
  6. 18
  7. 18
  8. 19
  9. 423
  10. 3
  11. 10
  12. 19
  13. 609
  14. 4
  15. 363
  16. 109
  17. 5
  18. 17
  19. 6
  20. 15
  21. 6
  22. 11
  23. 49
  24. 5
  25. 8
  26. 219
  27. 14
  28. 51
  29. 315
  30. 72
  31. 6
  32. 7
  33. 3
  34. 531
  35. 7
  36. 9
  37. 387
  38. 27
  39. 16
  40. 30

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