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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 415 · 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 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 478 (d) 600
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  6. 6.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 450 (d) 451
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 1 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  9. 9.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) 72 (c) 69 (d) 23
  10. 10.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 184 (d) 174
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  12. 12.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) 18 (d) 54
  13. 13.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 91 (d) 100
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
  15. 15.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 398 (c) 480 (d) 490
  16. 16.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 158 (c) 157 (d) 166
  17. 17.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) 30 (b) 81 (c) 9 (d) 27
  18. 18.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 138 (d) 137
  19. 19.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) 54 (c) 18 (d) 57
  20. 20.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) 21 (b) 66 (c) 189 (d) 63
  21. 21.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 147 (c) 148 (d) 156
  22. 22.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
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 4 (d) 14
  24. 24.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 285 (c) 295 (d) 294
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 3 (d) 4
  28. 28.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) 21 (c) 24 (d) 7
  29. 29.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) 237 (c) 238 (d) 228
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 15 (d) 6
  32. 32.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 76 (c) 85 (d) 94
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 15 (b) 16 (c) 13 (d) 9
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 2 (d) 3
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 5 (b) 2 (c) 4 (d) 3
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 5 (d) 4
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 4 (d) 5
  40. 40.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) 5 (b) 15 (c) 18 (d) 45

Answer key

  1. 609
  2. 3
  3. 5
  4. 19
  5. 8
  6. 450
  7. 3
  8. 6
  9. 69
  10. 183
  11. 4
  12. 18
  13. 91
  14. 15
  15. 489
  16. 157
  17. 27
  18. 137
  19. 54
  20. 63
  21. 147
  22. 36
  23. 15
  24. 294
  25. 7
  26. 18
  27. 4
  28. 21
  29. 237
  30. 9
  31. 16
  32. 85
  33. 19
  34. 15
  35. 4
  36. 4
  37. 4
  38. 17
  39. 5
  40. 15

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