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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 288 · 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 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) 27 (b) 24 (c) 72 (d) 8
  2. 2.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) 144 (b) 48 (c) 51 (d) 16
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 13 (c) 14 (d) 15
  4. 4.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 409 (c) 408 (d) 344
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 9 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 6 (b) 5 (c) 4 (d) 7
  9. 9.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 97 (c) 98 (d) 106
  10. 10.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 30 (c) 33 (d) 10
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
  12. 12.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) 45 (b) 18 (c) 5 (d) 15
  13. 13.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 594 (d) 595
  14. 14.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) 66 (b) 21 (c) 63 (d) 189
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  16. 16.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) 612 (c) 622 (d) 621
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  20. 20.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 346 (c) 302 (d) 345
  21. 21.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 102 (d) 94
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 18 (c) 16 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  24. 24.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) 21 (c) 54 (d) 6
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 15 (b) 4 (c) 16 (d) 14
  27. 27.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 87 (c) 78 (d) 88
  28. 28.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 631 (d) 492
  29. 29.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 458 (d) 579
  30. 30.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 146 (c) 128 (d) 138
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 15 (d) 4
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 20 (d) 19
  33. 33.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 68 (d) 86
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 4 (c) 5 (d) 3
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 9 (c) 6 (d) 7
  37. 37.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
  38. 38.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 492 (c) 501 (d) 406
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
  40. 40.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) 23 (c) 207 (d) 69

Answer key

  1. 24
  2. 48
  3. 14
  4. 408
  5. 19
  6. 3
  7. 4
  8. 6
  9. 97
  10. 30
  11. 17
  12. 15
  13. 594
  14. 63
  15. 3
  16. 621
  17. 2
  18. 6
  19. 8
  20. 345
  21. 93
  22. 17
  23. 5
  24. 18
  25. 3
  26. 15
  27. 87
  28. 630
  29. 579
  30. 137
  31. 15
  32. 19
  33. 77
  34. 4
  35. 7
  36. 8
  37. 33
  38. 501
  39. 3
  40. 69

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