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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 547 · 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 6 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 2 (d) 5
  2. 2.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 70 (d) 69
  3. 3.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) 216 (b) 24 (c) 75 (d) 72
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  5. 5.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 315 (c) 282 (d) 316
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 21
  7. 7.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) 198 (b) 66 (c) 69 (d) 22
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  12. 12.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) 348 (c) 415 (d) 405
  13. 13.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 348 (c) 310 (d) 357
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 19
  15. 15.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 171 (d) 180
  16. 16.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 490 (c) 398 (d) 489
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 2 (d) 3
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 2 (d) 5
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 1 (d) 3
  20. 20.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 307 (c) 276 (d) 306
  21. 21.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) 27 (d) 24
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  24. 24.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 166 (d) 158
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  26. 26.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 136 (c) 118 (d) 128
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15
  29. 29.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  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) 135 (b) 48 (c) 15 (d) 45
  32. 32.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 504 (c) 514 (d) 513
  33. 33.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
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 16 (d) 17
  35. 35.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
  36. 36.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 189 (c) 204 (d) 198
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 6 (d) 18
  38. 38.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) 45 (b) 15 (c) 18 (d) 5
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 15 (d) 16
  40. 40.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) 36 (b) 39 (c) 12 (d) 108

Answer key

  1. 4
  2. 69
  3. 72
  4. 8
  5. 315
  6. 20
  7. 66
  8. 2
  9. 7
  10. 9
  11. 3
  12. 414
  13. 357
  14. 18
  15. 171
  16. 489
  17. 4
  18. 4
  19. 3
  20. 306
  21. 24
  22. 18
  23. 4
  24. 157
  25. 3
  26. 127
  27. 20
  28. 15
  29. 2
  30. 7
  31. 45
  32. 513
  33. 18
  34. 16
  35. 237
  36. 198
  37. 17
  38. 15
  39. 15
  40. 36

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