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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 194 · 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 times is the digit 9 written when you write all the numbers from 1 to 81? (a) 6 (b) 8 (c) 7 (d) 9
  2. 2.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) 177 (c) 168 (d) 186
  3. 3.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 366 (d) 357
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 3 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 14 (c) 13 (d) 15
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 5 (b) 7 (c) 8 (d) 6
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  9. 9.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  11. 11.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 24 (d) 72
  12. 12.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) 24 (b) 7 (c) 21 (d) 63
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 15 (d) 14
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  15. 15.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) 45 (c) 126 (d) 14
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
  17. 17.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 264 (c) 254 (d) 274
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 21
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  20. 20.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 102 (d) 94
  21. 21.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5
  23. 23.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 585 (c) 468 (d) 595
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 14 (d) 15
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 12 (d) 3
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 18 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  29. 29.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 600 (c) 610 (d) 609
  30. 30.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) 10 (b) 90 (c) 33 (d) 30
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 7 (b) 9 (c) 8 (d) 6
  32. 32.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 190 (d) 189
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 17 (b) 16 (c) 7 (d) 18
  34. 34.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 77 (c) 78 (d) 68
  35. 35.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
  36. 36.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) 51 (c) 48 (d) 16
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 16 (d) 15
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 16 (d) 18
  39. 39.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 237 (c) 230 (d) 238
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3

Answer key

  1. 8
  2. 177
  3. 366
  4. 5
  5. 3
  6. 14
  7. 7
  8. 19
  9. 300
  10. 5
  11. 72
  12. 21
  13. 15
  14. 8
  15. 42
  16. 18
  17. 273
  18. 20
  19. 9
  20. 93
  21. 27
  22. 16
  23. 594
  24. 14
  25. 4
  26. 13
  27. 19
  28. 2
  29. 609
  30. 30
  31. 8
  32. 189
  33. 17
  34. 77
  35. 66
  36. 48
  37. 15
  38. 17
  39. 237
  40. 4

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