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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 591 · 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 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) 7 (d) 21
  2. 2.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 290 (c) 327 (d) 328
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 6 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 15 (d) 4
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 8 (d) 19
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 19 (d) 17
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 16 (b) 15 (c) 4 (d) 14
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 11 (b) 9 (c) 8 (d) 10
  12. 12.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 240 (c) 232 (d) 241
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 17 (c) 6 (d) 16
  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) 20 (b) 180 (c) 63 (d) 60
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  17. 17.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 131 (c) 132 (d) 140
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 1
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 7 (b) 11 (c) 13 (d) 14
  20. 20.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 148 (d) 140
  21. 21.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 198 (c) 180 (d) 190
  22. 22.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) 21 (b) 189 (c) 63 (d) 66
  23. 23.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 60 (d) 69
  24. 24.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 488 (c) 624 (d) 615
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 7 (c) 8 (d) 5
  26. 26.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 74 (c) 83 (d) 92
  27. 27.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 160 (c) 152 (d) 142
  28. 28.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) 171 (c) 60 (d) 57
  29. 29.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 465 (c) 474 (d) 388
  30. 30.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
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 5
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 1 (d) 3
  35. 35.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 58 (d) 40
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 5 (b) 4 (c) 6 (d) 3
  37. 37.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
  38. 38.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) 198 (c) 207 (d) 210
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18

Answer key

  1. 21
  2. 327
  3. 6
  4. 8
  5. 18
  6. 15
  7. 19
  8. 18
  9. 5
  10. 15
  11. 10
  12. 240
  13. 17
  14. 60
  15. 19
  16. 4
  17. 131
  18. 3
  19. 13
  20. 139
  21. 189
  22. 63
  23. 69
  24. 624
  25. 7
  26. 83
  27. 151
  28. 57
  29. 474
  30. 18
  31. 19
  32. 7
  33. 4
  34. 3
  35. 49
  36. 5
  37. 6
  38. 207
  39. 9
  40. 2

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