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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 330 · 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 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 259 (c) 258 (d) 249
  2. 2.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 36 (c) 45 (d) 54
  3. 3.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 135 (c) 15 (d) 45
  4. 4.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) 75 (b) 24 (c) 216 (d) 72
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 7 (d) 6
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  8. 8.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 525 (d) 516
  9. 9.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) 30 (c) 39 (d) 40
  10. 10.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 110 (c) 120 (d) 128
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  13. 13.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 159 (d) 160
  14. 14.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 146 (c) 136 (d) 154
  15. 15.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 445 (c) 368 (d) 435
  16. 16.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  17. 17.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) 17 (b) 51 (c) 54 (d) 153
  18. 18.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 56 (c) 48 (d) 38
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  20. 20.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 130 (c) 129 (d) 138
  21. 21.The numbers 10 to 18 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) 126 (c) 14 (d) 45
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 2 (c) 4 (d) 5
  23. 23.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) 8 (b) 72 (c) 24 (d) 27
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 2 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  30. 30.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
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  33. 33.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) 21 (b) 7 (c) 63 (d) 24
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 13 (b) 5 (c) 14 (d) 12
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 7 (b) 6 (c) 8 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 3 (d) 13
  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) 9 (b) 30 (c) 27 (d) 81
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  40. 40.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 90 (c) 100 (d) 99

Answer key

  1. 258
  2. 45
  3. 45
  4. 72
  5. 7
  6. 19
  7. 4
  8. 525
  9. 39
  10. 119
  11. 17
  12. 5
  13. 159
  14. 145
  15. 444
  16. 9
  17. 51
  18. 47
  19. 6
  20. 129
  21. 42
  22. 4
  23. 24
  24. 3
  25. 18
  26. 5
  27. 2
  28. 4
  29. 9
  30. 57
  31. 2
  32. 8
  33. 21
  34. 13
  35. 7
  36. 7
  37. 14
  38. 27
  39. 4
  40. 99

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