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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 148 · 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 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 17 (d) 15
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 15 (d) 16
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 15 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  9. 9.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 619 (d) 618
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 5 (d) 15
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 15 (b) 6 (c) 13 (d) 14
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
  14. 14.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) 137 (d) 128
  15. 15.The numbers 3 to 11 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) 21 (c) 24 (d) 7
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 18 (d) 7
  18. 18.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) 8 (c) 24 (d) 27
  19. 19.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 182 (c) 174 (d) 173
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
  21. 21.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 252 (d) 246
  22. 22.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 525 (c) 526 (d) 516
  23. 23.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) 21 (b) 54 (c) 18 (d) 6
  24. 24.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 60 (c) 69 (d) 70
  25. 25.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) 207 (b) 69 (c) 23 (d) 72
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 3 (d) 4
  27. 27.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) 171 (b) 57 (c) 60 (d) 19
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 20 (d) 19
  29. 29.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 91 (c) 100 (d) 92
  30. 30.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) 9 (b) 27 (c) 81 (d) 30
  31. 31.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 567 (c) 576 (d) 577
  32. 32.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) 5 (b) 15 (c) 18 (d) 45
  33. 33.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 283 (c) 273 (d) 260
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 4 (d) 3
  35. 35.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) 13 (c) 39 (d) 117
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 15 (c) 5 (d) 16
  38. 38.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 595 (d) 594
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 18 (d) 9

Answer key

  1. 16
  2. 8
  3. 5
  4. 16
  5. 3
  6. 9
  7. 14
  8. 2
  9. 618
  10. 7
  11. 15
  12. 14
  13. 19
  14. 137
  15. 21
  16. 20
  17. 18
  18. 24
  19. 173
  20. 3
  21. 261
  22. 525
  23. 18
  24. 69
  25. 69
  26. 5
  27. 57
  28. 19
  29. 91
  30. 27
  31. 576
  32. 15
  33. 282
  34. 5
  35. 39
  36. 19
  37. 15
  38. 594
  39. 6
  40. 19

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