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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 62 · 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 48? (a) 14 (b) 15 (c) 16 (d) 4
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  3. 3.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 282 (c) 315 (d) 316
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  5. 5.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 477 (c) 486 (d) 396
  6. 6.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 73 (c) 82 (d) 74
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 6 (b) 4 (c) 7 (d) 5
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 4 (c) 2 (d) 3
  11. 11.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) 108 (b) 12 (c) 39 (d) 36
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 14 (b) 4 (c) 15 (d) 13
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 15 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  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) 19 (b) 57 (c) 171 (d) 60
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  17. 17.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) 75 (b) 216 (c) 72 (d) 24
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 20 (d) 19
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18
  23. 23.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) 6 (c) 54 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 10 (b) 9 (c) 11 (d) 12
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 19 (d) 20
  28. 28.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) 72 (b) 207 (c) 23 (d) 69
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 9 (d) 20
  30. 30.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 110 (c) 120 (d) 128
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 4 (c) 16 (d) 14
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 7 (b) 8 (c) 5 (d) 6
  33. 33.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 394 (c) 474 (d) 484
  34. 34.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 294 (c) 285 (d) 268
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 5 (b) 7 (c) 6 (d) 8
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
  40. 40.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 552 (c) 446 (d) 562

Answer key

  1. 15
  2. 3
  3. 315
  4. 2
  5. 486
  6. 73
  7. 9
  8. 6
  9. 3
  10. 4
  11. 36
  12. 14
  13. 15
  14. 6
  15. 57
  16. 3
  17. 72
  18. 20
  19. 17
  20. 2
  21. 5
  22. 18
  23. 18
  24. 4
  25. 11
  26. 16
  27. 19
  28. 69
  29. 19
  30. 119
  31. 15
  32. 7
  33. 483
  34. 294
  35. 8
  36. 7
  37. 5
  38. 19
  39. 18
  40. 561

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