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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 707 · 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 9 written when you write all the numbers from 1 to 97? (a) 17 (b) 9 (c) 18 (d) 15
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 4 (d) 14
  3. 3.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 600 (c) 601 (d) 591
  4. 4.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) 24 (c) 7 (d) 21
  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) 5 (b) 15 (c) 18 (d) 45
  6. 6.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 166 (c) 157 (d) 158
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 17 (d) 16
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 6 (b) 5 (c) 3 (d) 4
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 14 (b) 6 (c) 16 (d) 15
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 6 (b) 5 (c) 4 (d) 3
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 5 (d) 4
  12. 12.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
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 17 (d) 16
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 13 (c) 15 (d) 16
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 4 (b) 5 (c) 7 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  19. 19.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) 54 (c) 162 (d) 57
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 19 (b) 18 (c) 7 (d) 17
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 5 (b) 4 (c) 2 (d) 3
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 2 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  24. 24.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) 81 (b) 9 (c) 27 (d) 30
  25. 25.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
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 19 (d) 8
  27. 27.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 140 (d) 148
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 15 (c) 16 (d) 17
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 6 (b) 9 (c) 7 (d) 8
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  34. 34.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 92 (c) 91 (d) 82
  35. 35.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 354 (c) 308 (d) 355
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  38. 38.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 490 (c) 398 (d) 489
  39. 39.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) 36 (c) 39 (d) 108
  40. 40.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) 72 (d) 23

Answer key

  1. 17
  2. 14
  3. 600
  4. 21
  5. 15
  6. 157
  7. 17
  8. 5
  9. 15
  10. 5
  11. 4
  12. 72
  13. 4
  14. 16
  15. 15
  16. 16
  17. 6
  18. 2
  19. 54
  20. 18
  21. 4
  22. 4
  23. 3
  24. 27
  25. 567
  26. 19
  27. 139
  28. 8
  29. 6
  30. 16
  31. 8
  32. 3
  33. 15
  34. 91
  35. 354
  36. 2
  37. 5
  38. 489
  39. 36
  40. 69

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