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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 261 · 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 two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  4. 4.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 180 (c) 179 (d) 170
  5. 5.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 525 (d) 535
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 8 (d) 18
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 1 (d) 4
  8. 8.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 414 (c) 513 (d) 514
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 14 (d) 16
  10. 10.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
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 18 (d) 19
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 12 (d) 13
  14. 14.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) 45 (b) 15 (c) 135 (d) 48
  15. 15.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 474 (c) 484 (d) 483
  16. 16.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) 63 (b) 60 (c) 180 (d) 20
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 17 (d) 8
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 19 (d) 20
  19. 19.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 160 (c) 151 (d) 152
  20. 20.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 101 (c) 102 (d) 110
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 16 (c) 15 (d) 5
  23. 23.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) 198 (c) 66 (d) 22
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
  25. 25.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) 42 (c) 117 (d) 13
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 16 (d) 15
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 16 (d) 15
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  29. 29.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 408 (c) 418 (d) 350
  30. 30.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 80 (c) 90 (d) 89
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 16 (d) 17
  32. 32.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 156 (c) 148 (d) 147
  33. 33.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 91 (c) 100 (d) 92
  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) 57 (b) 18 (c) 162 (d) 54
  35. 35.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 13 (b) 8 (c) 11 (d) 14
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 17 (d) 8
  39. 39.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) 23 (b) 72 (c) 207 (d) 69
  40. 40.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 328 (c) 375 (d) 384

Answer key

  1. 6
  2. 7
  3. 5
  4. 179
  5. 534
  6. 19
  7. 3
  8. 513
  9. 15
  10. 48
  11. 18
  12. 2
  13. 13
  14. 45
  15. 483
  16. 60
  17. 18
  18. 19
  19. 151
  20. 101
  21. 9
  22. 16
  23. 66
  24. 5
  25. 39
  26. 15
  27. 16
  28. 9
  29. 417
  30. 89
  31. 17
  32. 147
  33. 91
  34. 54
  35. 4
  36. 5
  37. 13
  38. 18
  39. 69
  40. 384

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