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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 759 · 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 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 376 (c) 456 (d) 447
  2. 2.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) 18 (c) 57 (d) 54
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  7. 7.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 356 (c) 417 (d) 426
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  9. 9.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 64 (c) 72 (d) 63
  10. 10.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 211 (d) 201
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  12. 12.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 370 (c) 438 (d) 448
  13. 13.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 81 (c) 72 (d) 82
  14. 14.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) 8 (c) 27 (d) 24
  15. 15.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 104 (c) 96 (d) 95
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 19 (d) 7
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  22. 22.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 156 (d) 155
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  25. 25.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 456 (c) 567 (d) 577
  26. 26.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) 54 (b) 18 (c) 6 (d) 21
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  28. 28.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 561 (c) 446 (d) 552
  29. 29.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) 189 (c) 63 (d) 21
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 5 (c) 4 (d) 6
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 20
  32. 32.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 286 (d) 322
  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) 17 (b) 54 (c) 51 (d) 153
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 15 (d) 4
  35. 35.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 98 (c) 80 (d) 89
  36. 36.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) 14 (b) 42 (c) 126 (d) 45
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 17 (d) 18
  38. 38.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) 5 (b) 15 (c) 45 (d) 18
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 5 (b) 6 (c) 4 (d) 7
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 18 (d) 20

Answer key

  1. 456
  2. 54
  3. 7
  4. 16
  5. 18
  6. 2
  7. 426
  8. 8
  9. 63
  10. 210
  11. 18
  12. 447
  13. 81
  14. 24
  15. 95
  16. 20
  17. 2
  18. 18
  19. 5
  20. 4
  21. 9
  22. 155
  23. 8
  24. 5
  25. 576
  26. 18
  27. 6
  28. 561
  29. 63
  30. 6
  31. 19
  32. 321
  33. 51
  34. 14
  35. 89
  36. 42
  37. 18
  38. 15
  39. 6
  40. 19

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