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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 717 · 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 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 2 (d) 4
  2. 2.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) 117 (b) 39 (c) 13 (d) 42
  3. 3.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) 36 (b) 12 (c) 39 (d) 108
  4. 4.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) 63 (d) 21
  5. 5.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 477 (c) 486 (d) 487
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 15 (b) 16 (c) 5 (d) 17
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 18 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  9. 9.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 71 (d) 72
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 3 (d) 4
  12. 12.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 164 (d) 163
  13. 13.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 436 (c) 547 (d) 537
  14. 14.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 182 (c) 174 (d) 173
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 17 (d) 16
  17. 17.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) 42 (b) 14 (c) 126 (d) 45
  18. 18.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 132 (c) 141 (d) 142
  19. 19.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 290 (c) 318 (d) 327
  20. 20.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 603 (d) 613
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 9 (d) 20
  22. 22.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
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 4 (d) 6
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 4 (b) 8 (c) 9 (d) 6
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  32. 32.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
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  34. 34.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) 18 (c) 54 (d) 57
  35. 35.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 456 (d) 576
  36. 36.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) 20 (c) 63 (d) 60
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  38. 38.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 549 (c) 558 (d) 444
  39. 39.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) 207 (c) 72 (d) 69
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7

Answer key

  1. 4
  2. 39
  3. 36
  4. 21
  5. 486
  6. 16
  7. 18
  8. 7
  9. 71
  10. 9
  11. 5
  12. 163
  13. 546
  14. 173
  15. 19
  16. 16
  17. 42
  18. 141
  19. 327
  20. 612
  21. 19
  22. 66
  23. 4
  24. 5
  25. 4
  26. 9
  27. 8
  28. 5
  29. 3
  30. 2
  31. 19
  32. 63
  33. 6
  34. 54
  35. 576
  36. 60
  37. 5
  38. 558
  39. 69
  40. 7

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