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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 667 · 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 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 426 (d) 427
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 15 (c) 16 (d) 14
  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) 18 (b) 5 (c) 15 (d) 45
  5. 5.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 594 (c) 603 (d) 474
  6. 6.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
  7. 7.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 65 (c) 66 (d) 74
  8. 8.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 418 (c) 408 (d) 350
  9. 9.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 643 (c) 633 (d) 500
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 19 (d) 18
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 16 (c) 14 (d) 4
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  15. 15.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) 27 (b) 30 (c) 9 (d) 81
  16. 16.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 351 (c) 306 (d) 342
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 4 (c) 14 (d) 13
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 20 (d) 19
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 18 (d) 19
  22. 22.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) 63 (b) 180 (c) 60 (d) 20
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 10 (c) 3 (d) 9
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 5 (d) 3
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 6 (c) 3 (d) 5
  26. 26.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) 66 (c) 22 (d) 69
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  29. 29.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 469 (d) 468
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 15 (c) 4 (d) 16
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  32. 32.The numbers 19 to 27 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) 69 (c) 207 (d) 23
  33. 33.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
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 12 (b) 8 (c) 11 (d) 9
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 5 (b) 6 (c) 4 (d) 3
  39. 39.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) 51 (b) 17 (c) 153 (d) 54
  40. 40.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 40 (c) 39 (d) 30

Answer key

  1. 426
  2. 18
  3. 15
  4. 15
  5. 603
  6. 36
  7. 65
  8. 417
  9. 642
  10. 6
  11. 4
  12. 19
  13. 15
  14. 18
  15. 27
  16. 351
  17. 14
  18. 9
  19. 19
  20. 7
  21. 18
  22. 60
  23. 10
  24. 5
  25. 5
  26. 66
  27. 5
  28. 17
  29. 468
  30. 15
  31. 5
  32. 69
  33. 73
  34. 2
  35. 8
  36. 4
  37. 11
  38. 5
  39. 51
  40. 39

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