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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 951 · 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 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 471 (c) 392 (d) 481
  2. 2.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 282 (d) 291
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  4. 4.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 434 (c) 543 (d) 544
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  7. 7.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 35 (d) 36
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  9. 9.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 334 (c) 324 (d) 333
  10. 10.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) 69 (b) 23 (c) 72 (d) 207
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 5 (d) 4
  12. 12.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 48 (c) 51 (d) 144
  13. 13.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 79 (c) 70 (d) 88
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  15. 15.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 376 (c) 375 (d) 366
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 5 (d) 4
  17. 17.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
  18. 18.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 454 (c) 564 (d) 574
  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) 57 (d) 18
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.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) 90 (b) 33 (c) 10 (d) 30
  23. 23.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) 189 (b) 66 (c) 21 (d) 63
  24. 24.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 498 (c) 508 (d) 507
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  26. 26.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) 54 (b) 153 (c) 17 (d) 51
  27. 27.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 154 (c) 136 (d) 145
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 4 (b) 3 (c) 2 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  31. 31.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
  32. 32.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) 9 (b) 81 (c) 30 (d) 27
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 3 (d) 13
  35. 35.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) 20 (c) 60 (d) 63
  36. 36.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 56 (c) 47 (d) 48
  37. 37.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 81 (d) 72
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 18
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 9 (c) 10 (d) 11
  40. 40.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 180 (c) 179 (d) 188

Answer key

  1. 480
  2. 291
  3. 8
  4. 543
  5. 9
  6. 7
  7. 35
  8. 5
  9. 333
  10. 69
  11. 6
  12. 48
  13. 79
  14. 8
  15. 375
  16. 6
  17. 24
  18. 573
  19. 54
  20. 20
  21. 4
  22. 30
  23. 63
  24. 507
  25. 6
  26. 51
  27. 145
  28. 2
  29. 4
  30. 7
  31. 39
  32. 27
  33. 19
  34. 13
  35. 60
  36. 47
  37. 81
  38. 19
  39. 10
  40. 179

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