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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 996 · 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 4 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 18 (d) 19
  2. 2.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
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  4. 4.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) 20 (b) 180 (c) 63 (d) 60
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 15 (d) 5
  6. 6.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 543 (c) 434 (d) 544
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 9 (b) 12 (c) 14 (d) 15
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 16 (d) 17
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 15 (b) 17 (c) 16 (d) 6
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 15 (b) 14 (c) 16 (d) 4
  11. 11.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 77 (c) 86 (d) 78
  12. 12.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 45 (d) 15
  13. 13.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 234 (c) 243 (d) 244
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  15. 15.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) 27 (b) 24 (c) 8 (d) 72
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  17. 17.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) 7 (b) 63 (c) 24 (d) 21
  18. 18.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) 126 (d) 14
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 3 (b) 4 (c) 1 (d) 2
  22. 22.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) 90 (c) 30 (d) 33
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 4 (d) 13
  24. 24.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 355 (c) 354 (d) 345
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 15 (b) 16 (c) 17 (d) 5
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 14 (c) 13 (d) 11
  27. 27.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 300 (d) 301
  28. 28.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  29. 29.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) 36 (d) 33
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 18 (d) 7
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 4 (b) 3 (c) 6 (d) 5
  32. 32.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 179 (c) 180 (d) 188
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 3 (c) 14 (d) 15
  34. 34.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) 54 (c) 162 (d) 57
  35. 35.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) 69 (b) 22 (c) 198 (d) 66
  36. 36.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 405 (d) 415
  37. 37.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 184 (c) 183 (d) 192
  38. 38.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) 118 (c) 126 (d) 117
  39. 39.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 60 (d) 50
  40. 40.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 493 (b) 400 (c) 492 (d) 483

Answer key

  1. 18
  2. 45
  3. 19
  4. 60
  5. 16
  6. 543
  7. 14
  8. 16
  9. 16
  10. 15
  11. 77
  12. 15
  13. 243
  14. 7
  15. 24
  16. 19
  17. 21
  18. 42
  19. 4
  20. 9
  21. 3
  22. 30
  23. 14
  24. 354
  25. 16
  26. 13
  27. 300
  28. 7
  29. 33
  30. 18
  31. 5
  32. 179
  33. 14
  34. 54
  35. 66
  36. 414
  37. 183
  38. 117
  39. 59
  40. 492

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