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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 245 · 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.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  2. 2.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 128 (c) 136 (d) 127
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 5 (d) 14
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 4 (d) 7
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 7 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  11. 11.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 400 (c) 492 (d) 493
  12. 12.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 210 (c) 220 (d) 219
  13. 13.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 477 (c) 396 (d) 486
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 7 (c) 5 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 15 (d) 16
  17. 17.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) 48 (b) 16 (c) 144 (d) 51
  18. 18.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 62 (d) 53
  19. 19.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) 153 (b) 51 (c) 54 (d) 17
  20. 20.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 38 (c) 47 (d) 48
  21. 21.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
  22. 22.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) 162 (b) 57 (c) 18 (d) 54
  23. 23.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
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 17
  29. 29.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 108 (c) 90 (d) 100
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 5 (d) 2
  31. 31.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 408 (c) 409 (d) 399
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 6 (b) 8 (c) 7 (d) 5
  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 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) 42 (b) 14 (c) 126 (d) 45
  35. 35.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 198 (d) 199
  36. 36.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 64 (c) 55 (d) 46
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 5 (c) 14 (d) 15
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 6 (d) 5
  39. 39.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
  40. 40.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 172 (c) 180 (d) 162

Answer key

  1. 6
  2. 127
  3. 4
  4. 8
  5. 8
  6. 7
  7. 15
  8. 6
  9. 7
  10. 3
  11. 492
  12. 219
  13. 486
  14. 7
  15. 3
  16. 15
  17. 48
  18. 53
  19. 51
  20. 47
  21. 33
  22. 54
  23. 87
  24. 9
  25. 2
  26. 7
  27. 5
  28. 18
  29. 99
  30. 4
  31. 408
  32. 7
  33. 9
  34. 42
  35. 198
  36. 55
  37. 15
  38. 5
  39. 39
  40. 171

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