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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 552 · 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 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 4 (c) 6 (d) 7
  2. 2.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) 8 (c) 24 (d) 72
  3. 3.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 95 (d) 86
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 3 (d) 1
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 21 (d) 20
  7. 7.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  9. 9.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 594 (c) 468 (d) 585
  10. 10.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
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 5 (d) 4
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 6 (d) 5
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 6 (d) 16
  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) 45 (c) 14 (d) 42
  15. 15.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 429 (d) 430
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  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) 51 (b) 16 (c) 48 (d) 144
  18. 18.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 48 (c) 56 (d) 47
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  20. 20.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 240 (d) 241
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 15 (b) 16 (c) 4 (d) 14
  22. 22.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 171 (d) 57
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 16 (b) 17 (c) 15 (d) 6
  24. 24.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) 63 (d) 21
  25. 25.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) 18 (b) 57 (c) 54 (d) 162
  26. 26.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 289 (c) 264 (d) 279
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 13 (d) 14
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 7 (b) 5 (c) 6 (d) 8
  33. 33.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 172 (c) 163 (d) 154
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 15 (d) 17
  35. 35.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 232 (d) 231
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 7 (d) 17
  38. 38.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) 45 (b) 15 (c) 135 (d) 48
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  40. 40.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) 39 (b) 42 (c) 13 (d) 117

Answer key

  1. 6
  2. 24
  3. 95
  4. 3
  5. 18
  6. 20
  7. 7
  8. 7
  9. 594
  10. 51
  11. 5
  12. 5
  13. 17
  14. 42
  15. 429
  16. 6
  17. 48
  18. 47
  19. 3
  20. 240
  21. 15
  22. 57
  23. 16
  24. 21
  25. 54
  26. 288
  27. 14
  28. 6
  29. 18
  30. 19
  31. 18
  32. 7
  33. 163
  34. 16
  35. 231
  36. 6
  37. 17
  38. 45
  39. 19
  40. 39

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