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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 736 · 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 11? (a) 8 (b) 7 (c) 12 (d) 9
  2. 2.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) 51 (b) 16 (c) 48 (d) 144
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
  4. 4.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) 21 (b) 66 (c) 189 (d) 63
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 7 (b) 19 (c) 17 (d) 18
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
  8. 8.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 501 (c) 510 (d) 511
  9. 9.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 495 (c) 505 (d) 504
  10. 10.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) 10 (c) 30 (d) 33
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  12. 12.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 579 (c) 588 (d) 464
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  14. 14.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) 39 (b) 12 (c) 108 (d) 36
  15. 15.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) 24 (c) 27 (d) 8
  16. 16.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 50 (c) 68 (d) 60
  17. 17.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 211 (d) 210
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 4 (b) 6 (c) 5 (d) 7
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 4 (d) 5
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  21. 21.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 46 (c) 45 (d) 54
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 19 (d) 8
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  25. 25.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 54 (d) 53
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 6 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 2 (d) 4
  29. 29.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 489 (c) 404 (d) 499
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 2 (d) 3
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 8 (d) 17
  33. 33.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) 17 (b) 153 (c) 51 (d) 54
  34. 34.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 568 (c) 567 (d) 558
  35. 35.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 338 (c) 399 (d) 400
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  37. 37.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 52 (c) 70 (d) 62
  38. 38.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 595 (d) 594
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  40. 40.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) 30 (b) 9 (c) 27 (d) 81

Answer key

  1. 8
  2. 48
  3. 17
  4. 63
  5. 5
  6. 18
  7. 18
  8. 510
  9. 504
  10. 30
  11. 2
  12. 588
  13. 15
  14. 36
  15. 24
  16. 59
  17. 210
  18. 6
  19. 4
  20. 18
  21. 45
  22. 18
  23. 6
  24. 7
  25. 53
  26. 17
  27. 3
  28. 4
  29. 498
  30. 4
  31. 5
  32. 18
  33. 51
  34. 567
  35. 399
  36. 17
  37. 61
  38. 594
  39. 4
  40. 27

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