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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 289 · 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.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) 22 (b) 69 (c) 66 (d) 198
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  5. 5.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 58 (c) 48 (d) 66
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 5 (d) 4
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 15 (d) 4
  8. 8.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 117 (c) 118 (d) 108
  9. 9.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 603 (d) 613
  10. 10.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) 19 (b) 57 (c) 171 (d) 60
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 14 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  14. 14.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
  15. 15.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 243 (d) 351
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  17. 17.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 426 (c) 362 (d) 435
  18. 18.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 78 (c) 60 (d) 70
  19. 19.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) 153 (b) 54 (c) 17 (d) 51
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 17 (d) 18
  24. 24.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) 30 (c) 81 (d) 27
  25. 25.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 306 (c) 352 (d) 351
  26. 26.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 247 (b) 237 (c) 246 (d) 236
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 2 (d) 3
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  29. 29.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 160 (c) 151 (d) 152
  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) 235 (b) 228 (c) 225 (d) 234
  31. 31.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) 36 (c) 39 (d) 12
  32. 32.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) 18 (b) 54 (c) 6 (d) 21
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 5 (b) 6 (c) 4 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
  37. 37.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) 72 (c) 81 (d) 82
  38. 38.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) 99 (c) 33 (d) 11
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 16 (d) 6
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 4 (b) 7 (c) 6 (d) 5

Answer key

  1. 66
  2. 16
  3. 4
  4. 8
  5. 57
  6. 4
  7. 15
  8. 117
  9. 612
  10. 57
  11. 15
  12. 5
  13. 16
  14. 60
  15. 243
  16. 6
  17. 435
  18. 69
  19. 51
  20. 4
  21. 8
  22. 6
  23. 17
  24. 27
  25. 351
  26. 246
  27. 4
  28. 16
  29. 151
  30. 234
  31. 36
  32. 18
  33. 5
  34. 3
  35. 20
  36. 19
  37. 81
  38. 33
  39. 17
  40. 6

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