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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 868 · 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 70? (a) 8 (b) 6 (c) 9 (d) 7
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 3 (b) 2 (c) 5 (d) 4
  3. 3.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) 23 (c) 69 (d) 207
  4. 4.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 89 (c) 90 (d) 98
  5. 5.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) 24 (b) 27 (c) 8 (d) 72
  6. 6.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 436 (c) 435 (d) 426
  7. 7.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
  8. 8.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 57 (d) 66
  9. 9.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 273 (c) 274 (d) 264
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  11. 11.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 96 (c) 86 (d) 95
  12. 12.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 429 (d) 438
  13. 13.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 408 (c) 409 (d) 344
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 6 (b) 4 (c) 5 (d) 7
  15. 15.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 185 (c) 186 (d) 194
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 7 (c) 6 (d) 8
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 19 (d) 20
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 15
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  23. 23.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 74 (c) 73 (d) 82
  24. 24.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) 57 (b) 54 (c) 18 (d) 162
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 14 (d) 15
  27. 27.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 434 (c) 534 (d) 544
  28. 28.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) 63 (c) 60 (d) 20
  29. 29.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) 66 (d) 189
  30. 30.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 39 (c) 40 (d) 48
  31. 31.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) 54 (c) 45 (d) 36
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  33. 33.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) 81 (d) 27
  34. 34.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) 18 (b) 5 (c) 45 (d) 15
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 16 (d) 17
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  37. 37.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) 33 (b) 90 (c) 10 (d) 30
  38. 38.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) 13 (b) 39 (c) 117 (d) 42
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 18 (b) 17 (c) 19 (d) 8

Answer key

  1. 8
  2. 4
  3. 69
  4. 89
  5. 24
  6. 435
  7. 42
  8. 57
  9. 273
  10. 5
  11. 95
  12. 438
  13. 408
  14. 6
  15. 185
  16. 7
  17. 2
  18. 3
  19. 19
  20. 16
  21. 7
  22. 9
  23. 73
  24. 54
  25. 5
  26. 15
  27. 543
  28. 60
  29. 63
  30. 39
  31. 45
  32. 9
  33. 27
  34. 15
  35. 17
  36. 20
  37. 30
  38. 39
  39. 4
  40. 18

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