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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 93 · 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 8 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 2 (d) 1
  3. 3.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 106 (c) 114 (d) 96
  4. 4.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 394 (c) 474 (d) 483
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  6. 6.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) 72 (b) 24 (c) 27 (d) 8
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 14 (c) 3 (d) 13
  8. 8.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) 48 (c) 135 (d) 15
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  10. 10.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 643 (c) 500 (d) 642
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 5 (d) 3
  12. 12.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 592 (c) 591 (d) 466
  13. 13.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) 18 (c) 6 (d) 54
  14. 14.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  16. 16.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 11 (d) 99
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  18. 18.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) 66 (c) 198 (d) 22
  19. 19.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 222 (d) 213
  20. 20.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 272 (c) 291 (d) 300
  21. 21.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) 15 (b) 18 (c) 5 (d) 45
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  28. 28.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 186 (c) 202 (d) 196
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 21 (d) 20
  31. 31.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) 153 (c) 51 (d) 17
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 5 (d) 6
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 19 (b) 18 (c) 20 (d) 9
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 7 (c) 9 (d) 8
  36. 36.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 517 (c) 507 (d) 516
  37. 37.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 88 (d) 79
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 3 (c) 13 (d) 14
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 5
  40. 40.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 502 (c) 492 (d) 501

Answer key

  1. 19
  2. 3
  3. 105
  4. 483
  5. 3
  6. 24
  7. 14
  8. 45
  9. 4
  10. 642
  11. 4
  12. 591
  13. 18
  14. 600
  15. 18
  16. 33
  17. 9
  18. 66
  19. 222
  20. 300
  21. 15
  22. 7
  23. 5
  24. 2
  25. 4
  26. 6
  27. 2
  28. 195
  29. 5
  30. 20
  31. 51
  32. 18
  33. 5
  34. 19
  35. 8
  36. 516
  37. 79
  38. 14
  39. 4
  40. 501

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