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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 824 · 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.

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  1. 1.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 441 (c) 372 (d) 451
  2. 2.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) 135 (c) 48 (d) 15
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 18 (d) 20
  4. 4.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 74 (d) 84
  5. 5.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 128 (c) 120 (d) 119
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 18 (d) 9
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 6 (b) 7 (c) 5 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  11. 11.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 90 (c) 80 (d) 98
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 15 (c) 13 (d) 14
  13. 13.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 189 (c) 198 (d) 190
  14. 14.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 91 (d) 82
  15. 15.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 156 (c) 165 (d) 174
  16. 16.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) 72 (b) 75 (c) 216 (d) 24
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 3 (c) 15 (d) 14
  18. 18.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 303 (d) 274
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
  20. 20.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 355 (c) 354 (d) 345
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 19 (d) 8
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 5 (d) 4
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
  25. 25.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 72 (c) 27 (d) 24
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 3 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  28. 28.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) 66 (d) 69
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 6 (d) 17
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 17 (d) 16
  31. 31.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 568 (d) 558
  32. 32.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) 153 (c) 17 (d) 54
  33. 33.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) 69 (d) 23
  34. 34.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) 21 (c) 63 (d) 189
  35. 35.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
  36. 36.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 474 (c) 465 (d) 388
  37. 37.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 62 (d) 70
  38. 38.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 344 (c) 399 (d) 408
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9

Answer key

  1. 450
  2. 45
  3. 19
  4. 83
  5. 119
  6. 19
  7. 6
  8. 5
  9. 9
  10. 8
  11. 89
  12. 14
  13. 189
  14. 91
  15. 165
  16. 72
  17. 14
  18. 303
  19. 18
  20. 354
  21. 19
  22. 19
  23. 5
  24. 4
  25. 24
  26. 5
  27. 7
  28. 66
  29. 17
  30. 16
  31. 567
  32. 51
  33. 69
  34. 63
  35. 30
  36. 474
  37. 61
  38. 408
  39. 6
  40. 20

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