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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 202 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
  2. 2.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 196 (c) 178 (d) 187
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 13 (c) 14 (d) 15
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 17 (d) 16
  5. 5.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 58 (c) 66 (d) 48
  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) 66 (b) 22 (c) 198 (d) 69
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 6 (b) 9 (c) 8 (d) 7
  8. 8.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
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 14 (c) 16 (d) 4
  10. 10.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 121 (c) 122 (d) 130
  11. 11.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 163 (d) 172
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 6 (b) 16 (c) 18 (d) 17
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 10 (b) 8 (c) 13 (d) 12
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  16. 16.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 264 (c) 254 (d) 274
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 4 (c) 6 (d) 5
  18. 18.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) 42 (b) 14 (c) 45 (d) 126
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 19 (d) 8
  20. 20.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 237 (c) 236 (d) 247
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 14 (d) 16
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 3 (d) 2
  25. 25.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) 57 (b) 18 (c) 54 (d) 162
  26. 26.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) 54 (b) 21 (c) 18 (d) 6
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 9 (b) 20 (c) 21 (d) 19
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  29. 29.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) 72 (b) 8 (c) 24 (d) 27
  30. 30.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 150 (c) 149 (d) 158
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 4 (d) 2
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 1 (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) 30 (b) 81 (c) 27 (d) 9
  37. 37.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 468 (d) 469
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 18 (b) 17 (c) 16 (d) 6
  40. 40.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 476 (c) 597 (d) 607

Answer key

  1. 17
  2. 187
  3. 14
  4. 16
  5. 57
  6. 66
  7. 8
  8. 69
  9. 15
  10. 121
  11. 163
  12. 17
  13. 4
  14. 12
  15. 3
  16. 273
  17. 6
  18. 42
  19. 19
  20. 246
  21. 5
  22. 15
  23. 7
  24. 3
  25. 54
  26. 18
  27. 20
  28. 19
  29. 24
  30. 149
  31. 5
  32. 9
  33. 3
  34. 7
  35. 3
  36. 27
  37. 468
  38. 3
  39. 17
  40. 606

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