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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 585 · 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 two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  2. 2.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) 27 (d) 30
  3. 3.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 163 (d) 154
  4. 4.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 75 (d) 76
  5. 5.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 528 (c) 537 (d) 430
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 7 (b) 5 (c) 8 (d) 6
  7. 7.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) 45 (b) 48 (c) 15 (d) 135
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 4 (c) 16 (d) 14
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 19 (d) 18
  10. 10.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 519 (d) 520
  11. 11.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 80 (c) 62 (d) 72
  12. 12.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 619 (d) 618
  13. 13.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 167 (c) 176 (d) 158
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 18 (d) 17
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  16. 16.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) 57 (c) 18 (d) 54
  17. 17.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) 42 (c) 45 (d) 126
  18. 18.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 110 (d) 92
  19. 19.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 6 (b) 5 (c) 8 (d) 7
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 17 (d) 16
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 18 (d) 16
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 17 (c) 18 (d) 6
  26. 26.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) 63 (b) 20 (c) 60 (d) 180
  27. 27.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 433 (c) 360 (d) 432
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  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) 24 (b) 8 (c) 72 (d) 27
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 14 (c) 3 (d) 15
  31. 31.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 573 (c) 564 (d) 454
  32. 32.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 114 (d) 132
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 6 (c) 5 (d) 3
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  35. 35.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 523 (c) 420 (d) 522
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  39. 39.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) 236 (c) 237 (d) 247
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 3 (d) 2

Answer key

  1. 5
  2. 27
  3. 163
  4. 75
  5. 537
  6. 7
  7. 45
  8. 15
  9. 18
  10. 519
  11. 71
  12. 618
  13. 167
  14. 18
  15. 5
  16. 54
  17. 42
  18. 101
  19. 4
  20. 5
  21. 7
  22. 19
  23. 17
  24. 17
  25. 17
  26. 60
  27. 432
  28. 9
  29. 24
  30. 14
  31. 573
  32. 123
  33. 5
  34. 18
  35. 522
  36. 20
  37. 20
  38. 4
  39. 246
  40. 3

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