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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 65 · 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 2 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  3. 3.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 46 (c) 28 (d) 37
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 3 (d) 2
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 1 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  7. 7.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 140 (d) 130
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 9 (d) 21
  9. 9.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) 30 (c) 27 (d) 81
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  11. 11.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) 69 (b) 198 (c) 66 (d) 22
  12. 12.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
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 2 (c) 4 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  15. 15.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) 558 (c) 567 (d) 450
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 16 (b) 14 (c) 15 (d) 4
  17. 17.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 135 (c) 144 (d) 126
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  19. 19.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 255 (c) 256 (d) 246
  20. 20.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) 126 (b) 45 (c) 42 (d) 14
  21. 21.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 352 (c) 421 (d) 411
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  23. 23.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
  24. 24.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) 89 (c) 90 (d) 80
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
  27. 27.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 119 (d) 110
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 13 (c) 3 (d) 14
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  31. 31.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) 5 (b) 15 (c) 45 (d) 18
  32. 32.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 432 (c) 540 (d) 531
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 18 (d) 20
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 15 (d) 6
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 17 (d) 8
  37. 37.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 375 (c) 384 (d) 328
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 19 (b) 17 (c) 18 (d) 8
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  40. 40.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) 48 (c) 16 (d) 144

Answer key

  1. 15
  2. 6
  3. 37
  4. 4
  5. 3
  6. 8
  7. 139
  8. 20
  9. 27
  10. 3
  11. 66
  12. 33
  13. 4
  14. 7
  15. 567
  16. 15
  17. 135
  18. 19
  19. 255
  20. 42
  21. 420
  22. 5
  23. 30
  24. 89
  25. 9
  26. 5
  27. 119
  28. 6
  29. 14
  30. 4
  31. 15
  32. 540
  33. 5
  34. 19
  35. 16
  36. 18
  37. 384
  38. 18
  39. 4
  40. 48

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