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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 659 · 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 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 4 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 15 (d) 5
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 5 (b) 3 (c) 4 (d) 2
  5. 5.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 486 (c) 621 (d) 622
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  7. 7.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) 57 (b) 60 (c) 171 (d) 19
  8. 8.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 62 (c) 70 (d) 52
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 6 (c) 5 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 20
  12. 12.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 375 (c) 385 (d) 384
  13. 13.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 142 (c) 152 (d) 151
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 18 (d) 16
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  16. 16.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 130 (c) 129 (d) 120
  17. 17.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 159 (c) 168 (d) 160
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 7 (b) 8 (c) 9 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  20. 20.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 86 (c) 76 (d) 94
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  22. 22.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) 69 (d) 207
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  24. 24.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 423 (c) 432 (d) 360
  25. 25.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 558 (d) 567
  26. 26.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) 39 (c) 12 (d) 36
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 5 (b) 2 (c) 3 (d) 4
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 10 (c) 8 (d) 9
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 18 (d) 6
  34. 34.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) 153 (c) 54 (d) 51
  35. 35.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) 27 (c) 24 (d) 72
  36. 36.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 357 (d) 348
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 4 (b) 5 (c) 6 (d) 7
  38. 38.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 588 (c) 597 (d) 470
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 15 (d) 5

Answer key

  1. 4
  2. 4
  3. 15
  4. 4
  5. 621
  6. 18
  7. 57
  8. 61
  9. 6
  10. 6
  11. 19
  12. 384
  13. 151
  14. 17
  15. 5
  16. 129
  17. 159
  18. 8
  19. 3
  20. 85
  21. 19
  22. 69
  23. 3
  24. 432
  25. 567
  26. 36
  27. 9
  28. 8
  29. 4
  30. 9
  31. 19
  32. 9
  33. 17
  34. 51
  35. 24
  36. 357
  37. 6
  38. 597
  39. 5
  40. 15

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