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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 669 · 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 7 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 2 (d) 1
  2. 2.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 120 (c) 102 (d) 111
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 20 (d) 21
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 4 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 4 (b) 5 (c) 6 (d) 3
  7. 7.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) 7 (b) 21 (c) 63 (d) 24
  8. 8.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 51 (d) 153
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 1 (d) 2
  11. 11.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 58 (c) 67 (d) 68
  12. 12.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) 6 (b) 21 (c) 54 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 5 (b) 2 (c) 4 (d) 3
  15. 15.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 307 (c) 306 (d) 276
  16. 16.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 102 (d) 101
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 19 (d) 18
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 7 (c) 8 (d) 9
  20. 20.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) 30 (d) 27
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  22. 22.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) 24 (b) 75 (c) 72 (d) 216
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 5 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 3 (d) 5
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 3 (d) 5
  27. 27.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 406 (c) 492 (d) 501
  28. 28.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) 19 (b) 171 (c) 60 (d) 57
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 17 (b) 18 (c) 8 (d) 19
  30. 30.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 537 (c) 528 (d) 430
  31. 31.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 61 (c) 70 (d) 52
  32. 32.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) 108 (c) 36 (d) 39
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  35. 35.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) 23 (b) 72 (c) 207 (d) 69
  36. 36.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 452 (d) 571
  37. 37.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 40 (c) 22 (d) 32
  38. 38.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 247 (c) 246 (d) 236
  39. 39.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) 189 (b) 21 (c) 63 (d) 66
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 15 (c) 16 (d) 14

Answer key

  1. 3
  2. 111
  3. 20
  4. 4
  5. 5
  6. 5
  7. 21
  8. 51
  9. 5
  10. 3
  11. 67
  12. 18
  13. 7
  14. 4
  15. 306
  16. 101
  17. 18
  18. 9
  19. 8
  20. 27
  21. 2
  22. 72
  23. 4
  24. 3
  25. 4
  26. 5
  27. 501
  28. 57
  29. 18
  30. 537
  31. 61
  32. 36
  33. 3
  34. 19
  35. 69
  36. 570
  37. 31
  38. 246
  39. 63
  40. 15

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