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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 107 · 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.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 396 (c) 342 (d) 405
  2. 2.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 318 (c) 360 (d) 370
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 10 (c) 13 (d) 12
  4. 4.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) 21 (b) 63 (c) 7 (d) 24
  5. 5.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) 21 (c) 54 (d) 18
  6. 6.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) 69 (b) 22 (c) 66 (d) 198
  7. 7.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) 189 (b) 63 (c) 66 (d) 21
  8. 8.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) 14 (b) 45 (c) 42 (d) 126
  9. 9.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) 51 (b) 54 (c) 153 (d) 17
  10. 10.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) 57 (c) 171 (d) 60
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 20 (d) 19
  14. 14.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) 69 (c) 72 (d) 23
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 5 (d) 2
  17. 17.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 349 (d) 348
  18. 18.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 91 (d) 82
  19. 19.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 162 (d) 171
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 6 (b) 4 (c) 9 (d) 8
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 16 (d) 17
  22. 22.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) 13 (b) 39 (c) 117 (d) 42
  23. 23.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 97 (c) 88 (d) 98
  24. 24.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 225 (d) 234
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 18 (d) 19
  26. 26.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 168 (c) 150 (d) 159
  27. 27.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 388 (c) 387 (d) 378
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  30. 30.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 72 (c) 54 (d) 63
  31. 31.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 211 (c) 212 (d) 210
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  33. 33.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 114 (d) 104
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 4 (b) 5 (c) 3 (d) 2
  35. 35.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 178 (c) 188 (d) 196
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 6 (d) 7
  37. 37.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 92 (d) 110
  38. 38.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 238 (c) 249 (d) 240
  39. 39.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) 99 (b) 36 (c) 33 (d) 11
  40. 40.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 61 (c) 70 (d) 52

Answer key

  1. 405
  2. 369
  3. 12
  4. 21
  5. 18
  6. 66
  7. 63
  8. 42
  9. 51
  10. 57
  11. 9
  12. 5
  13. 19
  14. 69
  15. 7
  16. 4
  17. 348
  18. 91
  19. 171
  20. 8
  21. 17
  22. 39
  23. 97
  24. 234
  25. 19
  26. 159
  27. 387
  28. 2
  29. 6
  30. 63
  31. 210
  32. 5
  33. 113
  34. 4
  35. 187
  36. 7
  37. 101
  38. 249
  39. 33
  40. 61

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