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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 718 · 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 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) 33 (c) 99 (d) 36
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 15 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  4. 4.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 496 (d) 636
  5. 5.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 499 (d) 489
  6. 6.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 162 (d) 18
  7. 7.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 95 (c) 86 (d) 96
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 7 (c) 8 (d) 6
  9. 9.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 172 (c) 164 (d) 154
  10. 10.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 366 (c) 316 (d) 367
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 18 (d) 9
  12. 12.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 56 (c) 55 (d) 46
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  14. 14.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) 14 (c) 45 (d) 42
  15. 15.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) 63 (c) 66 (d) 189
  16. 16.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 42 (d) 33
  17. 17.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) 20 (c) 180 (d) 60
  18. 18.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 573 (c) 574 (d) 454
  19. 19.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 48 (c) 39 (d) 40
  20. 20.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
  21. 21.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 309 (c) 310 (d) 278
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 7 (d) 6
  23. 23.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) 69 (b) 66 (c) 22 (d) 198
  24. 24.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 28 (c) 38 (d) 37
  25. 25.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 26 (c) 44 (d) 35
  26. 26.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 63 (c) 64 (d) 72
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 5 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  31. 31.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) 6 (c) 21 (d) 18
  32. 32.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 279 (d) 288
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 8 (c) 7 (d) 6
  35. 35.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 354 (c) 314 (d) 363
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 8 (d) 20
  38. 38.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) 15 (c) 18 (d) 5
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 9 (b) 7 (c) 6 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7

Answer key

  1. 33
  2. 15
  3. 5
  4. 636
  5. 498
  6. 54
  7. 95
  8. 7
  9. 163
  10. 366
  11. 19
  12. 55
  13. 3
  14. 42
  15. 63
  16. 33
  17. 60
  18. 573
  19. 39
  20. 51
  21. 309
  22. 6
  23. 66
  24. 37
  25. 35
  26. 63
  27. 8
  28. 3
  29. 5
  30. 7
  31. 18
  32. 288
  33. 3
  34. 8
  35. 363
  36. 3
  37. 19
  38. 15
  39. 8
  40. 7

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