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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 897 · 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 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 6 (d) 16
  2. 2.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) 54 (b) 17 (c) 153 (d) 51
  3. 3.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 36 (c) 26 (d) 35
  4. 4.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 168 (c) 176 (d) 167
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 6 (d) 18
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 8 (d) 17
  8. 8.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 138 (d) 137
  9. 9.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) 42 (b) 39 (c) 117 (d) 13
  10. 10.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 59 (d) 60
  11. 11.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 350 (c) 418 (d) 417
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  14. 14.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 292 (c) 330 (d) 321
  15. 15.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) 18 (b) 54 (c) 6 (d) 21
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  18. 18.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 499 (c) 489 (d) 404
  19. 19.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) 23 (c) 207 (d) 69
  20. 20.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) 54 (c) 18 (d) 57
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 20 (d) 18
  22. 22.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 255 (c) 242 (d) 256
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 4 (b) 7 (c) 6 (d) 5
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 3 (d) 6
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  26. 26.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) 48 (c) 135 (d) 45
  27. 27.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
  28. 28.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) 27 (b) 81 (c) 9 (d) 30
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  31. 31.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 391 (c) 381 (d) 390
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 5 (d) 7
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
  34. 34.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 362 (c) 436 (d) 435
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 16 (c) 6 (d) 17
  36. 36.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  38. 38.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) 60 (b) 20 (c) 63 (d) 180
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 5 (d) 4
  40. 40.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) 45 (b) 5 (c) 18 (d) 15

Answer key

  1. 17
  2. 51
  3. 35
  4. 167
  5. 5
  6. 17
  7. 18
  8. 137
  9. 39
  10. 59
  11. 417
  12. 7
  13. 6
  14. 330
  15. 18
  16. 20
  17. 9
  18. 498
  19. 69
  20. 54
  21. 19
  22. 255
  23. 6
  24. 5
  25. 2
  26. 45
  27. 36
  28. 27
  29. 18
  30. 4
  31. 390
  32. 7
  33. 20
  34. 435
  35. 16
  36. 123
  37. 3
  38. 60
  39. 4
  40. 15

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