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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 401 · 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 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 46 (c) 55 (d) 64
  2. 2.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 284 (c) 309 (d) 319
  3. 3.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) 18 (c) 57 (d) 54
  4. 4.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 32 (c) 22 (d) 31
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  6. 6.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 513 (c) 414 (d) 504
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  8. 8.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 267 (c) 276 (d) 277
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  11. 11.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 57 (d) 66
  12. 12.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) 51 (c) 153 (d) 54
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  15. 15.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) 72 (c) 27 (d) 8
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 16 (c) 6 (d) 18
  17. 17.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 68 (d) 86
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 19 (d) 20
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  20. 20.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) 90 (c) 30 (d) 33
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  26. 26.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) 23 (b) 207 (c) 72 (d) 69
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 13 (d) 14
  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.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 484 (c) 618 (d) 609
  30. 30.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 178 (c) 169 (d) 170
  31. 31.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) 15 (b) 45 (c) 135 (d) 48
  32. 32.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) 24 (c) 63 (d) 7
  33. 33.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 229 (c) 219 (d) 228
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 19 (d) 9
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 6 (d) 4
  36. 36.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
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 4 (d) 15
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  40. 40.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 402 (c) 412 (d) 411

Answer key

  1. 55
  2. 318
  3. 54
  4. 31
  5. 4
  6. 513
  7. 9
  8. 276
  9. 3
  10. 8
  11. 57
  12. 51
  13. 5
  14. 9
  15. 24
  16. 17
  17. 77
  18. 19
  19. 2
  20. 30
  21. 17
  22. 6
  23. 3
  24. 20
  25. 4
  26. 69
  27. 14
  28. 36
  29. 618
  30. 169
  31. 45
  32. 21
  33. 228
  34. 19
  35. 5
  36. 27
  37. 17
  38. 15
  39. 2
  40. 411

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