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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 761 · 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.

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  1. 1.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 40 (c) 32 (d) 31
  2. 2.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
  3. 3.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) 42 (c) 39 (d) 117
  4. 4.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 484 (d) 474
  5. 5.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 56 (d) 65
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  7. 7.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) 135 (b) 45 (c) 48 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 2 (d) 4
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 17 (c) 15 (d) 5
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 20
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 9 (c) 19 (d) 20
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  15. 15.The numbers 12 to 20 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) 51 (c) 144 (d) 16
  16. 16.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 405 (c) 415 (d) 348
  17. 17.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 132 (c) 131 (d) 122
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  19. 19.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 32 (c) 42 (d) 50
  20. 20.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 45 (d) 36
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  23. 23.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 160 (c) 159 (d) 168
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 7 (c) 8 (d) 5
  25. 25.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) 60 (b) 57 (c) 19 (d) 171
  26. 26.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) 24 (b) 27 (c) 8 (d) 72
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  28. 28.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 370 (c) 369 (d) 360
  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) 60 (b) 63 (c) 180 (d) 20
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 17 (d) 16
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
  33. 33.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) 18 (b) 57 (c) 162 (d) 54
  34. 34.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 448 (c) 565 (d) 564
  35. 35.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 132 (d) 114
  36. 36.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 186 (c) 176 (d) 185
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 18 (d) 6
  38. 38.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 342 (c) 352 (d) 351
  39. 39.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) 18 (b) 21 (c) 6 (d) 54
  40. 40.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 346 (d) 302

Answer key

  1. 31
  2. 21
  3. 39
  4. 483
  5. 65
  6. 6
  7. 45
  8. 3
  9. 4
  10. 16
  11. 19
  12. 20
  13. 20
  14. 3
  15. 48
  16. 414
  17. 131
  18. 8
  19. 41
  20. 45
  21. 3
  22. 16
  23. 159
  24. 7
  25. 57
  26. 24
  27. 5
  28. 369
  29. 60
  30. 4
  31. 16
  32. 15
  33. 54
  34. 564
  35. 123
  36. 185
  37. 17
  38. 351
  39. 18
  40. 345

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