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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 963 · 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) 7 (c) 63 (d) 21
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 5 (b) 8 (c) 6 (d) 7
  4. 4.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 432 (c) 423 (d) 360
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 8 (d) 19
  6. 6.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 158 (c) 157 (d) 166
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 12
  8. 8.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
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  10. 10.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 621 (c) 492 (d) 631
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  14. 14.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 139 (c) 130 (d) 148
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 20
  16. 16.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 64 (c) 82 (d) 74
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 15 (c) 3 (d) 13
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  21. 21.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) 82 (d) 81
  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) 72 (b) 24 (c) 75 (d) 216
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 3 (d) 2
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 12 (c) 14 (d) 13
  27. 27.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 210 (c) 220 (d) 218
  28. 28.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 166 (c) 165 (d) 174
  29. 29.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) 171 (c) 162 (d) 172
  30. 30.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) 51 (c) 54 (d) 153
  31. 31.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 80 (d) 90
  32. 32.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 612 (c) 613 (d) 603
  33. 33.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 110 (d) 120
  34. 34.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 414 (c) 354 (d) 423
  35. 35.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) 81 (b) 9 (c) 27 (d) 30
  36. 36.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 207 (c) 198 (d) 208
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 1 (d) 4
  38. 38.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 517 (d) 516
  39. 39.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 321 (c) 286 (d) 312
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2

Answer key

  1. 21
  2. 17
  3. 7
  4. 432
  5. 18
  6. 157
  7. 13
  8. 24
  9. 2
  10. 630
  11. 3
  12. 4
  13. 19
  14. 139
  15. 19
  16. 73
  17. 9
  18. 14
  19. 2
  20. 4
  21. 81
  22. 72
  23. 4
  24. 7
  25. 4
  26. 13
  27. 219
  28. 165
  29. 171
  30. 51
  31. 89
  32. 612
  33. 119
  34. 423
  35. 27
  36. 207
  37. 3
  38. 516
  39. 321
  40. 3

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