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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 172 · 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 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 630 (c) 639 (d) 640
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 3 (d) 4
  4. 4.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 570 (c) 571 (d) 561
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 4 (b) 6 (c) 5 (d) 7
  6. 6.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) 42 (c) 13 (d) 39
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  8. 8.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 40 (c) 31 (d) 22
  9. 9.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) 18 (c) 21 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 1 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  13. 13.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 212 (c) 210 (d) 211
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 17 (c) 15 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 6 (d) 7
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 4 (d) 2
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 19 (d) 20
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 4 (d) 15
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 15 (b) 7 (c) 17 (d) 16
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
  24. 24.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
  25. 25.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) 36 (b) 11 (c) 99 (d) 33
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 6 (d) 17
  27. 27.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) 108 (b) 36 (c) 12 (d) 39
  28. 28.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 57 (c) 19 (d) 60
  29. 29.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 95 (c) 104 (d) 86
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 19 (d) 18
  31. 31.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 448 (c) 370 (d) 438
  32. 32.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 535 (b) 534 (c) 525 (d) 428
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 20 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  37. 37.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 393 (c) 334 (d) 384
  38. 38.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 609 (c) 619 (d) 484
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 4 (c) 14 (d) 16
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15

Answer key

  1. 639
  2. 8
  3. 3
  4. 570
  5. 6
  6. 39
  7. 6
  8. 31
  9. 18
  10. 2
  11. 3
  12. 4
  13. 210
  14. 4
  15. 15
  16. 16
  17. 2
  18. 7
  19. 4
  20. 19
  21. 15
  22. 16
  23. 15
  24. 72
  25. 33
  26. 17
  27. 36
  28. 57
  29. 95
  30. 19
  31. 447
  32. 534
  33. 3
  34. 18
  35. 19
  36. 5
  37. 393
  38. 618
  39. 15
  40. 15

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