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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 181 · 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.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 207 (c) 210 (d) 198
  2. 2.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 162 (d) 171
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  5. 5.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 420 (c) 523 (d) 522
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 4 (b) 6 (c) 7 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  10. 10.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) 174 (c) 165 (d) 156
  11. 11.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) 207 (b) 23 (c) 69 (d) 72
  12. 12.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 495 (c) 505 (d) 408
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 9 (b) 6 (c) 7 (d) 8
  14. 14.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 432 (d) 541
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  16. 16.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 573 (c) 582 (d) 460
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  18. 18.The numbers 10 to 18 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) 45 (c) 126 (d) 14
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 4 (c) 3 (d) 7
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 3 (c) 13 (d) 14
  21. 21.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) 117 (c) 13 (d) 42
  22. 22.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) 24 (b) 75 (c) 72 (d) 216
  23. 23.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) 189 (b) 66 (c) 21 (d) 63
  24. 24.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 463 (c) 462 (d) 453
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  26. 26.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) 9 (b) 81 (c) 30 (d) 27
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 3 (b) 5 (c) 4 (d) 2
  28. 28.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) 129 (c) 130 (d) 120
  29. 29.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) 24 (c) 72 (d) 27
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 4 (d) 3
  31. 31.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 612 (c) 486 (d) 621
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  33. 33.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) 51 (c) 153 (d) 17
  34. 34.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) 30 (d) 90
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 6 (d) 16
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 6 (c) 5 (d) 4
  37. 37.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) 66 (b) 22 (c) 198 (d) 69
  38. 38.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) 54 (d) 6
  39. 39.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 110 (c) 109 (d) 100
  40. 40.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 50 (c) 49 (d) 40

Answer key

  1. 207
  2. 171
  3. 6
  4. 7
  5. 522
  6. 6
  7. 9
  8. 2
  9. 16
  10. 165
  11. 69
  12. 504
  13. 8
  14. 540
  15. 5
  16. 582
  17. 5
  18. 42
  19. 6
  20. 14
  21. 39
  22. 72
  23. 63
  24. 462
  25. 9
  26. 27
  27. 4
  28. 129
  29. 24
  30. 3
  31. 621
  32. 3
  33. 51
  34. 30
  35. 17
  36. 6
  37. 66
  38. 18
  39. 109
  40. 49

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