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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 956 · 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.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) 10 (c) 30 (d) 90
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 2 (d) 5
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 19 (b) 20 (c) 18 (d) 8
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 19 (d) 7
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 5 (d) 2
  7. 7.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 100 (d) 109
  8. 8.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 195 (c) 204 (d) 205
  9. 9.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 18 (d) 45
  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) 17 (b) 153 (c) 51 (d) 54
  11. 11.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) 30 (b) 81 (c) 27 (d) 9
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 4 (d) 3
  13. 13.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) 45 (c) 15 (d) 135
  14. 14.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 458 (c) 579 (d) 570
  15. 15.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) 12 (d) 36
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 5 (d) 16
  17. 17.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 198 (c) 210 (d) 208
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 14 (d) 15
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 6 (c) 5 (d) 4
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 7 (d) 19
  22. 22.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 69 (d) 23
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 9 (b) 7 (c) 6 (d) 8
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 19 (b) 18 (c) 9 (d) 20
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 7 (b) 11 (c) 9 (d) 12
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  27. 27.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
  28. 28.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 5 (d) 4
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
  31. 31.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) 57 (b) 60 (c) 19 (d) 171
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 18 (d) 20
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 3 (d) 5
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 4 (d) 1
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  38. 38.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 148 (c) 130 (d) 140
  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) 42 (b) 39 (c) 13 (d) 117
  40. 40.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 285 (c) 286 (d) 262

Answer key

  1. 30
  2. 6
  3. 4
  4. 19
  5. 18
  6. 4
  7. 109
  8. 204
  9. 15
  10. 51
  11. 27
  12. 4
  13. 45
  14. 579
  15. 36
  16. 16
  17. 207
  18. 15
  19. 8
  20. 6
  21. 18
  22. 69
  23. 8
  24. 19
  25. 11
  26. 17
  27. 21
  28. 7
  29. 6
  30. 18
  31. 57
  32. 6
  33. 19
  34. 5
  35. 4
  36. 3
  37. 2
  38. 139
  39. 39
  40. 285

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