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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 469 · 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 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 39 (c) 108 (d) 36
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 14 (c) 4 (d) 16
  3. 3.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 594 (c) 468 (d) 595
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 17 (d) 18
  5. 5.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 228 (c) 224 (d) 219
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  7. 7.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) 6 (c) 54 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  9. 9.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) 66 (b) 198 (c) 69 (d) 22
  10. 10.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 132 (c) 150 (d) 142
  11. 11.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 300 (d) 301
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 6 (c) 5 (d) 7
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 5 (d) 17
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  17. 17.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 129 (c) 130 (d) 120
  18. 18.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 380 (c) 453 (d) 463
  19. 19.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 582 (c) 591 (d) 466
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  23. 23.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) 180 (c) 60 (d) 20
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 4 (c) 5 (d) 6
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 8 (c) 6 (d) 7
  26. 26.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 104 (c) 113 (d) 114
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 20 (d) 8
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  29. 29.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) 63 (b) 24 (c) 7 (d) 21
  30. 30.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 558 (d) 567
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  32. 32.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 72 (c) 54 (d) 64
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  34. 34.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) 51 (b) 54 (c) 153 (d) 17
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 6 (d) 3
  37. 37.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 181 (c) 172 (d) 182
  38. 38.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 624 (c) 634 (d) 633
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 19 (b) 18 (c) 9 (d) 20

Answer key

  1. 36
  2. 15
  3. 594
  4. 18
  5. 228
  6. 18
  7. 18
  8. 3
  9. 66
  10. 141
  11. 300
  12. 15
  13. 6
  14. 16
  15. 4
  16. 18
  17. 129
  18. 462
  19. 591
  20. 17
  21. 7
  22. 2
  23. 60
  24. 6
  25. 8
  26. 113
  27. 19
  28. 5
  29. 21
  30. 567
  31. 8
  32. 63
  33. 9
  34. 51
  35. 5
  36. 5
  37. 181
  38. 633
  39. 3
  40. 19

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