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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 795 · 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 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 68 (d) 86
  2. 2.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) 108 (b) 12 (c) 39 (d) 36
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  4. 4.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 218 (c) 219 (d) 210
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 19 (d) 8
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 8 (d) 19
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 13 (d) 14
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 6 (b) 4 (c) 3 (d) 5
  10. 10.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 33 (c) 24 (d) 42
  11. 11.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) 57 (b) 171 (c) 60 (d) 19
  12. 12.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) 30 (b) 81 (c) 9 (d) 27
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  14. 14.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 500 (c) 642 (d) 643
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 2 (d) 3
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  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) 153 (c) 54 (d) 51
  18. 18.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 152 (c) 160 (d) 151
  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) 57 (c) 162 (d) 54
  20. 20.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) 30 (c) 90 (d) 33
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  22. 22.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 450 (c) 460 (d) 378
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 18 (d) 7
  24. 24.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 132 (c) 140 (d) 131
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  28. 28.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 117 (c) 126 (d) 118
  29. 29.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  31. 31.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 138 (d) 156
  32. 32.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 168 (d) 150
  33. 33.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 432 (c) 423 (d) 433
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 18 (d) 6
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 6 (c) 9 (d) 11
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  38. 38.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  39. 39.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
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 5 (b) 6 (c) 4 (d) 3

Answer key

  1. 77
  2. 36
  3. 3
  4. 219
  5. 6
  6. 19
  7. 18
  8. 14
  9. 5
  10. 33
  11. 57
  12. 27
  13. 6
  14. 642
  15. 4
  16. 4
  17. 51
  18. 151
  19. 54
  20. 30
  21. 3
  22. 459
  23. 17
  24. 131
  25. 5
  26. 2
  27. 4
  28. 117
  29. 8
  30. 18
  31. 147
  32. 159
  33. 432
  34. 8
  35. 17
  36. 11
  37. 4
  38. 81
  39. 33
  40. 5

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