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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 387 · 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 72? (a) 7 (b) 18 (c) 16 (d) 17
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 5 (c) 6 (d) 4
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 19 (d) 20
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  6. 6.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) 60 (b) 180 (c) 20 (d) 63
  7. 7.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) 144 (c) 16 (d) 51
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 5 (c) 12 (d) 13
  9. 9.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) 63 (b) 21 (c) 24 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 9 (c) 6 (d) 11
  12. 12.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 101 (d) 92
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 15 (d) 17
  14. 14.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 128 (c) 127 (d) 118
  15. 15.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) 57 (c) 60 (d) 19
  16. 16.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 85 (d) 94
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 18 (d) 20
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 4 (d) 2
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 5 (b) 6 (c) 7 (d) 4
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 8 (c) 6 (d) 7
  22. 22.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 164 (d) 163
  23. 23.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 26 (c) 35 (d) 44
  24. 24.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 66 (c) 22 (d) 69
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 13 (b) 14 (c) 15 (d) 4
  26. 26.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) 99 (c) 11 (d) 33
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 8 (d) 20
  28. 28.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) 15 (c) 45 (d) 48
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  30. 30.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 390 (c) 332 (d) 381
  31. 31.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
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 3 (b) 6 (c) 5 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  34. 34.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) 148 (d) 139
  35. 35.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 366 (c) 367 (d) 316
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 21 (d) 19
  37. 37.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) 72 (b) 216 (c) 75 (d) 24
  38. 38.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  39. 39.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  40. 40.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 583 (c) 573 (d) 460

Answer key

  1. 17
  2. 7
  3. 5
  4. 19
  5. 9
  6. 60
  7. 48
  8. 12
  9. 21
  10. 5
  11. 11
  12. 101
  13. 16
  14. 127
  15. 57
  16. 85
  17. 6
  18. 19
  19. 3
  20. 6
  21. 8
  22. 163
  23. 35
  24. 66
  25. 14
  26. 33
  27. 19
  28. 45
  29. 3
  30. 390
  31. 39
  32. 5
  33. 9
  34. 139
  35. 366
  36. 20
  37. 72
  38. 3
  39. 5
  40. 582

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