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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 89 · 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 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) 171 (c) 60 (d) 19
  2. 2.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 201 (d) 211
  3. 3.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 166 (c) 184 (d) 175
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17
  5. 5.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 535 (c) 534 (d) 525
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 5 (d) 3
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 20 (d) 19
  8. 8.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) 63 (b) 24 (c) 7 (d) 21
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 7 (b) 8 (c) 9 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  11. 11.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 234 (d) 228
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  13. 13.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) 45 (b) 5 (c) 18 (d) 15
  14. 14.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 91 (c) 82 (d) 92
  15. 15.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 222 (c) 213 (d) 220
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  17. 17.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 18 (c) 54 (d) 21
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  21. 21.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 178 (c) 177 (d) 168
  22. 22.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 571 (d) 452
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 18 (d) 19
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 16 (d) 15
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 16 (d) 15
  29. 29.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) 45 (b) 126 (c) 42 (d) 14
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 15 (d) 17
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 21 (b) 20 (c) 9 (d) 19
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  35. 35.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) 17 (c) 54 (d) 51
  36. 36.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 418 (c) 408 (d) 417
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
  38. 38.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 138 (c) 130 (d) 129
  39. 39.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) 30 (c) 33 (d) 90
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 5 (d) 3

Answer key

  1. 57
  2. 210
  3. 175
  4. 17
  5. 534
  6. 4
  7. 20
  8. 21
  9. 8
  10. 5
  11. 234
  12. 9
  13. 15
  14. 91
  15. 222
  16. 5
  17. 18
  18. 19
  19. 7
  20. 20
  21. 177
  22. 570
  23. 4
  24. 4
  25. 18
  26. 16
  27. 6
  28. 15
  29. 42
  30. 7
  31. 16
  32. 20
  33. 3
  34. 3
  35. 51
  36. 417
  37. 15
  38. 129
  39. 30
  40. 4

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