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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 606 · 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.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 19 (d) 20
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 8 (b) 6 (c) 5 (d) 7
  4. 4.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) 72 (b) 69 (c) 23 (d) 207
  5. 5.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 15 (d) 45
  6. 6.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 176 (c) 168 (d) 167
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 13 (c) 14 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 5 (b) 3 (c) 6 (d) 4
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 4 (b) 8 (c) 6 (d) 9
  11. 11.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 122 (d) 104
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 3 (d) 6
  13. 13.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 490 (c) 480 (d) 398
  14. 14.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 154 (d) 163
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  18. 18.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) 66 (c) 69 (d) 198
  19. 19.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 70 (c) 79 (d) 88
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 5 (b) 16 (c) 17 (d) 15
  22. 22.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 411 (c) 420 (d) 421
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 15 (d) 5
  24. 24.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 52 (d) 61
  25. 25.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 405 (c) 342 (d) 406
  26. 26.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 46 (d) 54
  27. 27.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) 126 (b) 42 (c) 14 (d) 45
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 17 (d) 18
  29. 29.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 612 (c) 486 (d) 622
  30. 30.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) 15 (b) 5 (c) 18 (d) 45
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
  32. 32.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 573 (c) 454 (d) 564
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 17 (d) 16
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 6 (d) 4
  35. 35.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 226 (d) 222
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 7 (b) 5 (c) 6 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  38. 38.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 190 (c) 182 (d) 181
  39. 39.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 576 (d) 456
  40. 40.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 48 (c) 51 (d) 144

Answer key

  1. 21
  2. 19
  3. 7
  4. 69
  5. 45
  6. 167
  7. 14
  8. 7
  9. 5
  10. 8
  11. 113
  12. 5
  13. 489
  14. 163
  15. 2
  16. 18
  17. 9
  18. 66
  19. 79
  20. 8
  21. 16
  22. 420
  23. 16
  24. 61
  25. 405
  26. 45
  27. 42
  28. 17
  29. 621
  30. 15
  31. 19
  32. 573
  33. 17
  34. 5
  35. 231
  36. 6
  37. 7
  38. 181
  39. 576
  40. 48

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