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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 719 · 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 4? (a) 3 (b) 5 (c) 4 (d) 10
  2. 2.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 454 (c) 453 (d) 374
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 20 (d) 21
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 6
  5. 5.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
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 6 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  8. 8.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) 189 (b) 66 (c) 63 (d) 21
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  10. 10.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) 18 (c) 6 (d) 54
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  12. 12.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 411 (c) 346 (d) 412
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 13 (d) 14
  14. 14.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) 42 (d) 39
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  16. 16.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) 48 (b) 135 (c) 45 (d) 15
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 5 (d) 4
  20. 20.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) 21 (b) 63 (c) 24 (d) 7
  21. 21.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 228 (d) 234
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  23. 23.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 50 (c) 68 (d) 59
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 14 (c) 13 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  26. 26.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 176 (c) 186 (d) 194
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 4 (c) 5 (d) 7
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 16 (b) 15 (c) 17 (d) 6
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 5 (c) 6 (d) 4
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 19 (d) 20
  31. 31.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 41 (c) 42 (d) 50
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  33. 33.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  34. 34.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 318 (c) 327 (d) 290
  35. 35.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) 396 (c) 477 (d) 486
  36. 36.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
  37. 37.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 634 (c) 633 (d) 494
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 17 (d) 16
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 3 (d) 4
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 6 (c) 8 (d) 7

Answer key

  1. 4
  2. 453
  3. 20
  4. 5
  5. 24
  6. 17
  7. 4
  8. 63
  9. 20
  10. 18
  11. 2
  12. 411
  13. 14
  14. 39
  15. 7
  16. 45
  17. 8
  18. 9
  19. 4
  20. 21
  21. 234
  22. 9
  23. 59
  24. 14
  25. 6
  26. 185
  27. 6
  28. 16
  29. 5
  30. 20
  31. 41
  32. 3
  33. 177
  34. 327
  35. 486
  36. 15
  37. 633
  38. 16
  39. 4
  40. 7

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