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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 228 · 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 times is the digit 9 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 1 (d) 3
  2. 2.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) 45 (b) 15 (c) 18 (d) 5
  3. 3.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) 12 (b) 108 (c) 36 (d) 39
  4. 4.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 368 (c) 445 (d) 435
  5. 5.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) 30 (b) 90 (c) 10 (d) 33
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 2 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 13 (b) 15 (c) 3 (d) 14
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 19 (d) 18
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 17
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 14 (b) 15 (c) 13 (d) 6
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 5 (d) 2
  15. 15.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 80 (c) 90 (d) 89
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 5 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 17
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
  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) 7 (d) 8
  22. 22.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 74 (c) 64 (d) 82
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  24. 24.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) 72 (c) 90 (d) 81
  25. 25.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 296 (c) 337 (d) 327
  26. 26.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) 45 (b) 42 (c) 14 (d) 126
  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) 30 (b) 81 (c) 9 (d) 27
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 17 (d) 16
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 19 (d) 18
  30. 30.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
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 8 (d) 20
  33. 33.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 579 (d) 580
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 18 (d) 20
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  36. 36.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
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  38. 38.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 543 (c) 440 (d) 553
  39. 39.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  40. 40.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) 33 (c) 11 (d) 99

Answer key

  1. 3
  2. 15
  3. 36
  4. 444
  5. 30
  6. 3
  7. 5
  8. 3
  9. 6
  10. 14
  11. 19
  12. 18
  13. 14
  14. 4
  15. 89
  16. 20
  17. 5
  18. 2
  19. 18
  20. 18
  21. 7
  22. 73
  23. 3
  24. 81
  25. 336
  26. 42
  27. 27
  28. 16
  29. 19
  30. 24
  31. 8
  32. 19
  33. 579
  34. 19
  35. 9
  36. 543
  37. 9
  38. 552
  39. 6
  40. 33

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