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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 928 · 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.The numbers 12 to 20 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) 16 (c) 144 (d) 51
  2. 2.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 84 (c) 66 (d) 75
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 7 (c) 11 (d) 13
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 17 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  7. 7.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) 153 (b) 54 (c) 51 (d) 17
  8. 8.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) 171 (b) 19 (c) 57 (d) 60
  9. 9.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) 15 (b) 135 (c) 45 (d) 48
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 17 (d) 16
  11. 11.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) 162 (b) 18 (c) 57 (d) 54
  12. 12.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) 36 (b) 12 (c) 108 (d) 39
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  14. 14.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 125 (c) 126 (d) 116
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  16. 16.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 399 (c) 408 (d) 409
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  19. 19.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 582 (c) 583 (d) 573
  20. 20.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 487 (c) 486 (d) 477
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 15 (d) 4
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 4 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 17 (b) 18 (c) 6 (d) 16
  26. 26.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) 39 (b) 13 (c) 42 (d) 117
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 16 (d) 15
  28. 28.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 20 (d) 63
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 6 (b) 8 (c) 7 (d) 5
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
  31. 31.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 55 (c) 46 (d) 56
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 7 (b) 19 (c) 18 (d) 17
  34. 34.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) 72 (c) 69 (d) 23
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 5 (c) 3 (d) 4
  36. 36.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 88 (d) 97
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  38. 38.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 552 (c) 561 (d) 562
  39. 39.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 128 (c) 127 (d) 136
  40. 40.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 103 (c) 112 (d) 104

Answer key

  1. 48
  2. 75
  3. 13
  4. 17
  5. 3
  6. 9
  7. 51
  8. 57
  9. 45
  10. 17
  11. 54
  12. 36
  13. 19
  14. 125
  15. 9
  16. 408
  17. 5
  18. 7
  19. 582
  20. 486
  21. 15
  22. 5
  23. 8
  24. 2
  25. 17
  26. 39
  27. 16
  28. 60
  29. 7
  30. 5
  31. 55
  32. 6
  33. 18
  34. 69
  35. 4
  36. 97
  37. 5
  38. 561
  39. 127
  40. 103

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