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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 774 · 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 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) 162 (b) 54 (c) 57 (d) 18
  2. 2.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 176 (c) 175 (d) 184
  3. 3.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 166 (c) 148 (d) 158
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  7. 7.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) 27 (c) 30 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  10. 10.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 462 (c) 586 (d) 585
  11. 11.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 96 (d) 95
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 3 (c) 15 (d) 14
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 12 (c) 14 (d) 13
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 6 (d) 7
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 13 (c) 15 (d) 14
  20. 20.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) 198 (b) 22 (c) 69 (d) 66
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  22. 22.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 132 (c) 131 (d) 140
  23. 23.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 264 (c) 254 (d) 273
  24. 24.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) 18 (c) 45 (d) 15
  25. 25.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 11 (c) 99 (d) 33
  26. 26.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 60 (c) 68 (d) 59
  27. 27.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  28. 28.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) 39 (b) 12 (c) 36 (d) 108
  29. 29.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) 180 (c) 20 (d) 60
  30. 30.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 493 (c) 492 (d) 483
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 5
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 4 (d) 6
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  35. 35.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) 13 (c) 117 (d) 42
  36. 36.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 210 (c) 220 (d) 219
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  38. 38.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 262 (c) 252 (d) 246
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 6 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10

Answer key

  1. 54
  2. 175
  3. 157
  4. 3
  5. 5
  6. 6
  7. 27
  8. 7
  9. 9
  10. 585
  11. 95
  12. 14
  13. 4
  14. 3
  15. 6
  16. 13
  17. 20
  18. 6
  19. 14
  20. 66
  21. 8
  22. 131
  23. 273
  24. 15
  25. 33
  26. 59
  27. 7
  28. 36
  29. 60
  30. 492
  31. 3
  32. 4
  33. 5
  34. 9
  35. 39
  36. 219
  37. 19
  38. 261
  39. 6
  40. 2

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