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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 526 · 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 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 612 (d) 621
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  3. 3.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 52 (c) 43 (d) 34
  4. 4.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 72 (c) 80 (d) 62
  5. 5.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 54 (d) 36
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  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) 171 (b) 60 (c) 57 (d) 19
  8. 8.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) 11 (b) 36 (c) 33 (d) 99
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  12. 12.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) 216 (b) 75 (c) 24 (d) 72
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 16 (c) 15 (d) 5
  16. 16.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 427 (d) 426
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  18. 18.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 399 (c) 409 (d) 344
  19. 19.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) 45 (b) 126 (c) 42 (d) 14
  20. 20.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
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  22. 22.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) 69 (c) 198 (d) 22
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  24. 24.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) 54 (c) 18 (d) 57
  25. 25.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 312 (c) 351 (d) 360
  26. 26.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
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 5 (c) 7 (d) 6
  30. 30.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 235 (c) 228 (d) 225
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 17 (d) 7
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 4 (d) 7
  34. 34.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 53 (c) 54 (d) 62
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
  36. 36.The numbers 3 to 11 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) 63 (c) 21 (d) 7
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  38. 38.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 176 (c) 158 (d) 167
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 19 (d) 9
  40. 40.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 543 (c) 553 (d) 440

Answer key

  1. 621
  2. 9
  3. 43
  4. 71
  5. 45
  6. 6
  7. 57
  8. 33
  9. 18
  10. 2
  11. 8
  12. 72
  13. 19
  14. 7
  15. 15
  16. 426
  17. 3
  18. 408
  19. 42
  20. 69
  21. 2
  22. 66
  23. 9
  24. 54
  25. 360
  26. 24
  27. 4
  28. 5
  29. 6
  30. 234
  31. 3
  32. 18
  33. 6
  34. 53
  35. 19
  36. 21
  37. 8
  38. 167
  39. 20
  40. 552

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