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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 523 · 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 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  3. 3.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) 72 (b) 27 (c) 24 (d) 8
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 14 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  7. 7.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 148 (c) 147 (d) 138
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  9. 9.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 501 (c) 492 (d) 502
  10. 10.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 298 (c) 330 (d) 340
  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) 24 (c) 72 (d) 75
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 15 (d) 4
  13. 13.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
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 8 (c) 18 (d) 17
  15. 15.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) 33 (b) 90 (c) 30 (d) 10
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 4 (c) 6 (d) 7
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 13 (c) 9 (d) 15
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  19. 19.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 612 (c) 621 (d) 486
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 17 (d) 7
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  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) 171 (b) 60 (c) 19 (d) 57
  23. 23.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) 54 (b) 57 (c) 162 (d) 18
  24. 24.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 240 (c) 250 (d) 238
  25. 25.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) 108 (b) 39 (c) 36 (d) 12
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 17 (c) 19 (d) 18
  27. 27.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 51 (c) 42 (d) 52
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 6 (b) 4 (c) 7 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 6 (b) 8 (c) 7 (d) 5
  31. 31.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) 66 (b) 63 (c) 21 (d) 189
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 11 (b) 12 (c) 9 (d) 8
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 17 (d) 5
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  35. 35.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) 15 (b) 48 (c) 45 (d) 135
  36. 36.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) 45 (d) 126
  37. 37.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) 9 (b) 30 (c) 27 (d) 81
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  39. 39.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) 60 (c) 180 (d) 20
  40. 40.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 513 (c) 523 (d) 522

Answer key

  1. 19
  2. 9
  3. 24
  4. 19
  5. 15
  6. 7
  7. 147
  8. 4
  9. 501
  10. 339
  11. 72
  12. 15
  13. 21
  14. 18
  15. 30
  16. 6
  17. 15
  18. 9
  19. 621
  20. 18
  21. 5
  22. 57
  23. 54
  24. 249
  25. 36
  26. 18
  27. 51
  28. 6
  29. 2
  30. 7
  31. 63
  32. 11
  33. 16
  34. 3
  35. 45
  36. 42
  37. 27
  38. 3
  39. 60
  40. 522

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