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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 444 · 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 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) 36 (c) 108 (d) 12
  2. 2.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 165 (c) 156 (d) 166
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  4. 4.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) 51 (d) 54
  5. 5.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
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 14 (b) 13 (c) 4 (d) 15
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19
  11. 11.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 79 (c) 80 (d) 88
  12. 12.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 252 (c) 240 (d) 253
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  14. 14.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) 180 (b) 60 (c) 63 (d) 20
  15. 15.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 5 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 9 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  21. 21.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 238 (c) 237 (d) 228
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  23. 23.The numbers 20 to 28 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) 216 (c) 72 (d) 75
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  25. 25.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 619 (c) 484 (d) 618
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 7 (c) 18 (d) 17
  27. 27.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 74 (c) 73 (d) 82
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  29. 29.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) 30 (b) 10 (c) 90 (d) 33
  30. 30.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 420 (d) 523
  31. 31.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 448 (c) 555 (d) 565
  32. 32.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 310 (d) 309
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 9 (b) 20 (c) 19 (d) 18
  34. 34.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 140 (d) 148
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  36. 36.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) 21 (b) 6 (c) 54 (d) 18
  37. 37.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 113 (c) 104 (d) 114
  38. 38.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 456 (d) 457
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 16 (d) 14
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 7 (d) 6

Answer key

  1. 36
  2. 165
  3. 8
  4. 51
  5. 42
  6. 5
  7. 4
  8. 4
  9. 14
  10. 19
  11. 79
  12. 252
  13. 5
  14. 60
  15. 177
  16. 4
  17. 2
  18. 9
  19. 19
  20. 9
  21. 237
  22. 7
  23. 72
  24. 6
  25. 618
  26. 18
  27. 73
  28. 3
  29. 30
  30. 522
  31. 564
  32. 309
  33. 19
  34. 139
  35. 8
  36. 18
  37. 113
  38. 456
  39. 15
  40. 6

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