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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 847 · 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 1 written when you write all the numbers from 1 to 51? (a) 17 (b) 5 (c) 16 (d) 15
  2. 2.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) 75 (b) 24 (c) 72 (d) 216
  3. 3.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) 54 (b) 153 (c) 17 (d) 51
  4. 4.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) 15 (b) 135 (c) 45 (d) 48
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 3 (c) 5 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  7. 7.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 112 (c) 130 (d) 122
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 1 (c) 2 (d) 4
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 5 (d) 2
  10. 10.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) 108 (b) 39 (c) 36 (d) 12
  11. 11.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) 126 (c) 42 (d) 14
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  13. 13.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) 18 (c) 21 (d) 54
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 16 (b) 17 (c) 6 (d) 18
  17. 17.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) 306 (c) 307 (d) 276
  18. 18.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 442 (c) 441 (d) 366
  19. 19.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 535 (b) 525 (c) 534 (d) 428
  20. 20.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 241 (d) 240
  21. 21.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 112 (d) 111
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 6 (c) 7 (d) 5
  23. 23.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 517 (c) 516 (d) 416
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 14 (b) 11 (c) 9 (d) 13
  25. 25.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) 117 (c) 39 (d) 42
  26. 26.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 105 (c) 106 (d) 114
  27. 27.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) 11 (b) 36 (c) 33 (d) 99
  28. 28.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
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  30. 30.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) 5 (b) 15 (c) 18 (d) 45
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 19 (d) 20
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 15 (d) 14
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 19 (d) 20
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 5 (b) 3 (c) 4 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  39. 39.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 162 (c) 171 (d) 172
  40. 40.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

Answer key

  1. 16
  2. 72
  3. 51
  4. 45
  5. 5
  6. 8
  7. 121
  8. 3
  9. 4
  10. 36
  11. 42
  12. 9
  13. 18
  14. 3
  15. 4
  16. 17
  17. 306
  18. 441
  19. 534
  20. 240
  21. 111
  22. 7
  23. 516
  24. 13
  25. 39
  26. 105
  27. 33
  28. 39
  29. 7
  30. 15
  31. 19
  32. 15
  33. 19
  34. 5
  35. 3
  36. 6
  37. 2
  38. 20
  39. 171
  40. 54

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