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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 327 · 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.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 54 (d) 36
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  3. 3.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 65 (c) 74 (d) 66
  4. 4.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) 10 (b) 30 (c) 33 (d) 90
  5. 5.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) 63 (c) 189 (d) 66
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  7. 7.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 186 (c) 196 (d) 195
  8. 8.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) 99 (c) 11 (d) 33
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 18 (d) 17
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 6 (d) 5
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 16 (d) 7
  15. 15.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) 60 (b) 57 (c) 19 (d) 171
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 3 (d) 6
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 19 (d) 17
  18. 18.The numbers 19 to 27 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) 69 (c) 23 (d) 207
  19. 19.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) 54 (b) 21 (c) 18 (d) 6
  20. 20.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) 130 (d) 140
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  24. 24.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 58 (d) 57
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 4 (b) 3 (c) 5 (d) 6
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 17 (b) 15 (c) 6 (d) 16
  28. 28.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  30. 30.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 163 (d) 164
  31. 31.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 75 (d) 24
  32. 32.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 159 (c) 160 (d) 168
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  34. 34.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 201 (c) 202 (d) 192
  35. 35.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) 39 (c) 108 (d) 36
  36. 36.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) 135 (b) 15 (c) 48 (d) 45
  37. 37.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 336 (c) 396 (d) 397
  38. 38.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) 60 (c) 20 (d) 63
  39. 39.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 376 (c) 456 (d) 457
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

  1. 45
  2. 8
  3. 65
  4. 30
  5. 63
  6. 7
  7. 195
  8. 33
  9. 4
  10. 19
  11. 18
  12. 4
  13. 5
  14. 17
  15. 57
  16. 5
  17. 18
  18. 69
  19. 18
  20. 139
  21. 2
  22. 6
  23. 8
  24. 57
  25. 5
  26. 2
  27. 16
  28. 5
  29. 9
  30. 163
  31. 72
  32. 159
  33. 3
  34. 201
  35. 36
  36. 45
  37. 396
  38. 60
  39. 456
  40. 4

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