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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 447 · 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 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 322 (c) 366 (d) 376
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 9 (b) 11 (c) 6 (d) 12
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 7 (c) 5 (d) 8
  6. 6.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
  7. 7.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) 126 (c) 45 (d) 42
  8. 8.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 634 (c) 633 (d) 494
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 4 (d) 14
  11. 11.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) 69 (c) 23 (d) 72
  12. 12.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 480 (c) 392 (d) 471
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 19 (d) 7
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 5 (d) 4
  15. 15.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) 15 (b) 45 (c) 48 (d) 135
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  17. 17.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
  19. 19.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) 18 (b) 5 (c) 15 (d) 45
  20. 20.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) 8 (b) 72 (c) 27 (d) 24
  21. 21.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) 20 (b) 180 (c) 63 (d) 60
  22. 22.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 628 (c) 490 (d) 627
  23. 23.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 124 (c) 134 (d) 133
  24. 24.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 426 (c) 522 (d) 532
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 17 (d) 18
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 20 (d) 8
  27. 27.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) 81 (b) 27 (c) 30 (d) 9
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 3 (d) 2
  30. 30.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 32 (c) 40 (d) 22
  31. 31.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 552 (c) 543 (d) 440
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 7 (d) 17
  34. 34.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 86 (d) 94
  35. 35.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 595 (d) 594
  36. 36.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 446 (c) 562 (d) 561
  37. 37.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 78 (d) 87
  38. 38.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) 166 (c) 156 (d) 165
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 16 (d) 15
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6

Answer key

  1. 375
  2. 3
  3. 11
  4. 7
  5. 7
  6. 33
  7. 42
  8. 633
  9. 2
  10. 15
  11. 69
  12. 480
  13. 18
  14. 4
  15. 45
  16. 9
  17. 8
  18. 18
  19. 15
  20. 24
  21. 60
  22. 627
  23. 133
  24. 531
  25. 18
  26. 19
  27. 27
  28. 5
  29. 3
  30. 31
  31. 552
  32. 4
  33. 18
  34. 85
  35. 594
  36. 561
  37. 87
  38. 165
  39. 15
  40. 7

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