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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 976 · 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 52? (a) 16 (b) 5 (c) 14 (d) 15
  2. 2.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 199 (c) 204 (d) 189
  3. 3.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 27 (d) 9
  4. 4.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) 21 (b) 63 (c) 189 (d) 66
  5. 5.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) 117 (d) 42
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  7. 7.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) 66 (d) 198
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  10. 10.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 624 (d) 625
  11. 11.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  12. 12.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) 19 (c) 171 (d) 57
  13. 13.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 458 (c) 579 (d) 580
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 18 (c) 6 (d) 16
  15. 15.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 448 (c) 370 (d) 438
  16. 16.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) 57 (c) 18 (d) 54
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  18. 18.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 54 (c) 18 (d) 6
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 8 (c) 7 (d) 5
  20. 20.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 44 (c) 36 (d) 35
  21. 21.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) 14 (b) 42 (c) 126 (d) 45
  22. 22.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) 48 (d) 45
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 15 (c) 3 (d) 14
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  26. 26.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 291 (c) 266 (d) 292
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  28. 28.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) 17 (b) 51 (c) 153 (d) 54
  29. 29.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) 163 (c) 164 (d) 172
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 9 (d) 19
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 7 (b) 9 (c) 6 (d) 8
  33. 33.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) 155 (c) 146 (d) 164
  34. 34.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 326 (c) 381 (d) 372
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 17 (b) 8 (c) 18 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  38. 38.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 404 (c) 489 (d) 498
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7

Answer key

  1. 15
  2. 198
  3. 27
  4. 63
  5. 39
  6. 5
  7. 66
  8. 4
  9. 4
  10. 624
  11. 117
  12. 57
  13. 579
  14. 17
  15. 447
  16. 54
  17. 9
  18. 18
  19. 7
  20. 35
  21. 42
  22. 45
  23. 14
  24. 2
  25. 6
  26. 291
  27. 17
  28. 51
  29. 163
  30. 5
  31. 20
  32. 8
  33. 155
  34. 381
  35. 18
  36. 7
  37. 3
  38. 498
  39. 9
  40. 8

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