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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 222 · 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 45? (a) 14 (b) 4 (c) 16 (d) 15
  2. 2.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) 36 (c) 39 (d) 108
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 19 (d) 8
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 19 (d) 18
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 11 (c) 13 (d) 7
  8. 8.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 57 (c) 54 (d) 162
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  10. 10.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 220 (c) 210 (d) 219
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 19 (d) 9
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 11 (b) 12 (c) 13 (d) 4
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 14 (d) 15
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 5 (d) 6
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 16 (d) 18
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  20. 20.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 597 (c) 598 (d) 470
  21. 21.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 157 (c) 158 (d) 166
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 13 (c) 15 (d) 14
  24. 24.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) 21 (b) 6 (c) 54 (d) 18
  25. 25.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 24 (c) 7 (d) 21
  26. 26.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 126 (c) 125 (d) 116
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 6 (c) 4 (d) 5
  28. 28.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 252 (d) 246
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 14 (d) 5
  30. 30.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) 20 (b) 180 (c) 60 (d) 63
  31. 31.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) 42 (b) 13 (c) 39 (d) 117
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  33. 33.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 564 (c) 448 (d) 555
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 5 (d) 4
  35. 35.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) 57 (b) 19 (c) 171 (d) 60
  36. 36.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 604 (c) 474 (d) 594
  37. 37.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 94 (c) 103 (d) 112
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3

Answer key

  1. 15
  2. 36
  3. 5
  4. 5
  5. 19
  6. 18
  7. 13
  8. 54
  9. 9
  10. 219
  11. 18
  12. 19
  13. 12
  14. 15
  15. 6
  16. 18
  17. 3
  18. 6
  19. 7
  20. 597
  21. 157
  22. 15
  23. 14
  24. 18
  25. 21
  26. 125
  27. 6
  28. 261
  29. 15
  30. 60
  31. 39
  32. 4
  33. 564
  34. 5
  35. 57
  36. 603
  37. 103
  38. 2
  39. 2
  40. 4

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