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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 880 · 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 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 19 (d) 8
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 4 (c) 5 (d) 6
  3. 3.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) 30 (b) 90 (c) 33 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 4 (c) 3 (d) 7
  6. 6.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) 171 (b) 57 (c) 60 (d) 19
  7. 7.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 150 (d) 141
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 12 (b) 8 (c) 9 (d) 11
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  11. 11.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 547 (c) 436 (d) 546
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 15 (d) 14
  13. 13.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 108 (c) 126 (d) 117
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 6 (b) 4 (c) 7 (d) 5
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 20 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  17. 17.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) 207 (d) 69
  18. 18.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
  19. 19.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 171 (d) 180
  20. 20.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) 24 (b) 7 (c) 21 (d) 63
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 21
  24. 24.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 261 (c) 271 (d) 252
  25. 25.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) 189 (c) 66 (d) 63
  26. 26.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 594 (c) 474 (d) 604
  27. 27.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
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 16 (d) 17
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 19 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 5 (c) 7 (d) 6
  32. 32.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) 54 (c) 57 (d) 162
  33. 33.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 116 (c) 124 (d) 115
  34. 34.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 519 (c) 528 (d) 529
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 5 (d) 2
  36. 36.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) 69 (b) 66 (c) 22 (d) 198
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 5 (d) 3
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

  1. 18
  2. 6
  3. 30
  4. 3
  5. 6
  6. 57
  7. 141
  8. 5
  9. 11
  10. 4
  11. 546
  12. 14
  13. 117
  14. 6
  15. 19
  16. 4
  17. 69
  18. 207
  19. 171
  20. 21
  21. 7
  22. 2
  23. 20
  24. 270
  25. 63
  26. 603
  27. 27
  28. 17
  29. 19
  30. 8
  31. 7
  32. 54
  33. 115
  34. 528
  35. 4
  36. 66
  37. 5
  38. 4
  39. 19
  40. 3

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