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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 204 · 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 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 6 (c) 4 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  3. 3.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 574 (c) 573 (d) 454
  4. 4.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) 162 (b) 57 (c) 54 (d) 18
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 2 (d) 3
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 3 (c) 14 (d) 13
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 16 (c) 15 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  12. 12.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) 60 (c) 180 (d) 63
  13. 13.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 255 (c) 265 (d) 264
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 21
  15. 15.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 205 (c) 195 (d) 208
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  18. 18.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) 22 (b) 198 (c) 69 (d) 66
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 17 (c) 15 (d) 16
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 18 (c) 16 (d) 17
  21. 21.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) 81 (b) 9 (c) 27 (d) 30
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 6 (d) 17
  23. 23.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) 99 (b) 11 (c) 36 (d) 33
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  26. 26.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 339 (c) 304 (d) 348
  27. 27.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) 48 (c) 45 (d) 15
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 2 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 6 (d) 3
  31. 31.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) 72 (b) 27 (c) 8 (d) 24
  32. 32.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 155 (d) 156
  33. 33.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 163 (d) 154
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  35. 35.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 472 (c) 601 (d) 591
  36. 36.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
  37. 37.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 390 (c) 381 (d) 332
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 17 (d) 5
  39. 39.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) 18 (c) 21 (d) 6
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 4 (d) 3

Answer key

  1. 5
  2. 4
  3. 573
  4. 54
  5. 4
  6. 14
  7. 16
  8. 8
  9. 6
  10. 7
  11. 18
  12. 60
  13. 264
  14. 20
  15. 204
  16. 7
  17. 15
  18. 66
  19. 16
  20. 17
  21. 27
  22. 17
  23. 33
  24. 4
  25. 20
  26. 348
  27. 45
  28. 4
  29. 9
  30. 5
  31. 24
  32. 155
  33. 163
  34. 2
  35. 600
  36. 42
  37. 390
  38. 16
  39. 18
  40. 5

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