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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 219 · 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 41? (a) 3 (b) 2 (c) 4 (d) 5
  2. 2.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 136 (c) 145 (d) 146
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 11 (c) 13 (d) 3
  6. 6.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 504 (c) 414 (d) 513
  7. 7.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 333 (c) 343 (d) 342
  8. 8.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) 99 (b) 33 (c) 11 (d) 36
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  10. 10.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 53 (c) 54 (d) 62
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 2 (c) 3 (d) 4
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  13. 13.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 144 (d) 153
  14. 14.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 404 (c) 498 (d) 489
  15. 15.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
  16. 16.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 516 (d) 507
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 20 (d) 18
  19. 19.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) 10 (b) 90 (c) 30 (d) 33
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 8 (d) 20
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 15 (b) 14 (c) 16 (d) 5
  23. 23.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) 69 (d) 207
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 19 (b) 17 (c) 8 (d) 18
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 2 (c) 4 (d) 3
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 14 (b) 16 (c) 15 (d) 4
  28. 28.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) 66 (b) 69 (c) 198 (d) 22
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 5 (b) 7 (c) 6 (d) 4
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 6 (b) 18 (c) 17 (d) 16
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 17 (d) 18
  32. 32.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 224 (c) 228 (d) 219
  33. 33.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
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 18 (d) 16
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
  38. 38.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) 63 (b) 7 (c) 21 (d) 24
  39. 39.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) 45 (c) 5 (d) 15
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 16 (d) 17

Answer key

  1. 4
  2. 145
  3. 6
  4. 4
  5. 12
  6. 513
  7. 342
  8. 33
  9. 7
  10. 53
  11. 4
  12. 19
  13. 153
  14. 498
  15. 60
  16. 516
  17. 9
  18. 19
  19. 30
  20. 19
  21. 6
  22. 15
  23. 69
  24. 5
  25. 18
  26. 4
  27. 15
  28. 66
  29. 6
  30. 17
  31. 18
  32. 228
  33. 18
  34. 2
  35. 2
  36. 17
  37. 4
  38. 21
  39. 15
  40. 17

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