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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 898 · 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) 12 (b) 7 (c) 9 (d) 8
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 15 (d) 4
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 18
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 4 (d) 5
  5. 5.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) 180 (b) 63 (c) 20 (d) 60
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  7. 7.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) 189 (c) 66 (d) 63
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  9. 9.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) 33 (b) 90 (c) 10 (d) 30
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  11. 11.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) 19 (c) 60 (d) 57
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 1 (d) 3
  13. 13.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 66 (c) 56 (d) 74
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 10 (c) 11 (d) 4
  16. 16.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 450 (d) 558
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
  19. 19.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 438 (c) 549 (d) 540
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  21. 21.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
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 4 (d) 5
  23. 23.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 22 (c) 69 (d) 198
  24. 24.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 43 (c) 34 (d) 44
  25. 25.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 123 (c) 132 (d) 124
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 5 (d) 4
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 3 (c) 5 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 3 (b) 15 (c) 14 (d) 13
  30. 30.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 291 (c) 272 (d) 300
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  33. 33.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) 48 (c) 135 (d) 45
  34. 34.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 519 (c) 529 (d) 528
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  36. 36.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 144 (c) 136 (d) 135
  37. 37.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 141 (c) 132 (d) 150
  38. 38.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 57 (d) 66
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (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) 27 (b) 9 (c) 30 (d) 81

Answer key

  1. 8
  2. 15
  3. 17
  4. 4
  5. 60
  6. 3
  7. 63
  8. 5
  9. 30
  10. 19
  11. 57
  12. 3
  13. 65
  14. 6
  15. 10
  16. 567
  17. 15
  18. 3
  19. 549
  20. 4
  21. 15
  22. 6
  23. 66
  24. 43
  25. 123
  26. 5
  27. 5
  28. 9
  29. 14
  30. 300
  31. 9
  32. 7
  33. 45
  34. 528
  35. 7
  36. 135
  37. 141
  38. 57
  39. 2
  40. 27

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