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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 51 · 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 9 written when you write all the numbers from 1 to 47? (a) 4 (b) 2 (c) 3 (d) 5
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 4 (d) 5
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 6 (b) 7 (c) 8 (d) 5
  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 two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  6. 6.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) 66 (b) 189 (c) 21 (d) 63
  7. 7.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) 15 (b) 45 (c) 18 (d) 5
  8. 8.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 74 (c) 83 (d) 92
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 5 (d) 16
  10. 10.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 279 (c) 264 (d) 288
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  12. 12.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 408 (c) 505 (d) 495
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 13 (c) 14 (d) 15
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  15. 15.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) 51 (b) 17 (c) 54 (d) 153
  16. 16.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 306 (c) 282 (d) 315
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 10 (b) 8 (c) 7 (d) 9
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 15 (b) 16 (c) 14 (d) 4
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  22. 22.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) 51 (c) 16 (d) 144
  23. 23.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 622 (c) 621 (d) 486
  24. 24.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) 57 (d) 162
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 3 (c) 4 (d) 5
  27. 27.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 56 (c) 48 (d) 38
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 18 (d) 20
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  30. 30.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) 13 (b) 117 (c) 39 (d) 42
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  34. 34.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 552 (c) 561 (d) 446
  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) 198 (b) 22 (c) 69 (d) 66
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 17 (d) 16
  37. 37.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) 139 (c) 148 (d) 130
  38. 38.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 207 (d) 198
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 16 (b) 4 (c) 15 (d) 14
  40. 40.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) 39 (b) 12 (c) 108 (d) 36

Answer key

  1. 4
  2. 4
  3. 7
  4. 60
  5. 6
  6. 63
  7. 15
  8. 83
  9. 16
  10. 288
  11. 9
  12. 504
  13. 14
  14. 3
  15. 51
  16. 315
  17. 7
  18. 4
  19. 9
  20. 15
  21. 18
  22. 48
  23. 621
  24. 54
  25. 9
  26. 5
  27. 47
  28. 19
  29. 6
  30. 39
  31. 20
  32. 20
  33. 8
  34. 561
  35. 66
  36. 16
  37. 139
  38. 207
  39. 15
  40. 36

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