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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 747 · 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 3 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 4 (d) 13
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  3. 3.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 559 (c) 549 (d) 558
  4. 4.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) 6 (b) 54 (c) 21 (d) 18
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  6. 6.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 348 (d) 357
  7. 7.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) 30 (c) 27 (d) 81
  8. 8.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  9. 9.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) 128 (c) 137 (d) 146
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 5 (b) 3 (c) 4 (d) 2
  13. 13.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) 23 (c) 72 (d) 69
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  16. 16.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 99 (d) 11
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 18 (d) 20
  19. 19.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 412 (c) 411 (d) 402
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 9 (b) 7 (c) 8 (d) 10
  21. 21.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) 130 (c) 139 (d) 148
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 15 (d) 14
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 19 (d) 17
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 6 (d) 5
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 4 (d) 5
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 17 (d) 19
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 11 (c) 10 (d) 3
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 13 (c) 11 (d) 3
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 8 (b) 5 (c) 7 (d) 6
  30. 30.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) 10 (b) 33 (c) 30 (d) 90
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 13 (c) 14 (d) 3
  32. 32.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 478 (d) 609
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 17 (d) 16
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  36. 36.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) 19 (b) 60 (c) 171 (d) 57
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 7 (b) 6 (c) 4 (d) 5
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 19 (d) 8
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19

Answer key

  1. 14
  2. 6
  3. 558
  4. 18
  5. 7
  6. 357
  7. 27
  8. 3
  9. 137
  10. 19
  11. 5
  12. 4
  13. 69
  14. 6
  15. 5
  16. 33
  17. 4
  18. 19
  19. 411
  20. 9
  21. 139
  22. 15
  23. 18
  24. 6
  25. 6
  26. 18
  27. 11
  28. 12
  29. 7
  30. 30
  31. 14
  32. 609
  33. 7
  34. 17
  35. 8
  36. 57
  37. 6
  38. 19
  39. 8
  40. 19

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