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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 826 · 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.

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  1. 1.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 52 (c) 34 (d) 44
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  4. 4.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 250 (c) 267 (d) 258
  5. 5.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 84 (c) 83 (d) 92
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  8. 8.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) 135 (b) 48 (c) 15 (d) 45
  9. 9.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) 117 (b) 13 (c) 42 (d) 39
  10. 10.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 105 (c) 114 (d) 106
  11. 11.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 582 (c) 592 (d) 466
  12. 12.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
  13. 13.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  14. 14.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) 60 (b) 57 (c) 19 (d) 171
  15. 15.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) 69 (b) 72 (c) 23 (d) 207
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 4 (c) 3 (d) 5
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 18 (d) 17
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  21. 21.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 488 (c) 624 (d) 615
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  23. 23.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 628 (d) 627
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 11 (b) 8 (c) 5 (d) 10
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  26. 26.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) 45 (c) 14 (d) 126
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 11 (b) 12 (c) 13 (d) 4
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 20 (d) 19
  29. 29.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 155 (d) 146
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  31. 31.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) 108 (c) 39 (d) 36
  32. 32.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) 99 (b) 11 (c) 33 (d) 36
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  34. 34.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 63 (c) 21 (d) 66
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 5 (d) 17
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 5 (b) 4 (c) 6 (d) 3
  39. 39.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 306 (c) 297 (d) 307
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17

Answer key

  1. 43
  2. 20
  3. 2
  4. 267
  5. 83
  6. 3
  7. 6
  8. 45
  9. 39
  10. 105
  11. 591
  12. 24
  13. 123
  14. 57
  15. 69
  16. 4
  17. 4
  18. 17
  19. 18
  20. 2
  21. 624
  22. 4
  23. 627
  24. 10
  25. 6
  26. 42
  27. 12
  28. 20
  29. 155
  30. 7
  31. 36
  32. 33
  33. 17
  34. 63
  35. 16
  36. 3
  37. 5
  38. 5
  39. 306
  40. 17

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