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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 877 · 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 two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 3 (c) 13 (d) 14
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 5 (b) 6 (c) 4 (d) 7
  4. 4.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 202 (d) 201
  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) 487 (b) 396 (c) 486 (d) 477
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 4 (d) 2
  8. 8.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) 135 (b) 48 (c) 15 (d) 45
  9. 9.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 618 (c) 619 (d) 484
  10. 10.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) 57 (b) 171 (c) 19 (d) 60
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 20 (c) 8 (d) 19
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  14. 14.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) 21 (b) 18 (c) 54 (d) 6
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 18 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  17. 17.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 48 (d) 144
  18. 18.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 80 (c) 70 (d) 88
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  20. 20.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 498 (c) 410 (d) 507
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  22. 22.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) 27 (b) 81 (c) 30 (d) 9
  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) 69 (b) 23 (c) 207 (d) 72
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 17 (b) 19 (c) 8 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 17 (d) 18
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 3 (d) 4
  29. 29.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) 30 (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) 45 (b) 15 (c) 18 (d) 5
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 16 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  33. 33.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 246 (c) 236 (d) 247
  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) 18 (b) 54 (c) 162 (d) 57
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 6 (c) 7 (d) 5
  36. 36.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 340 (c) 330 (d) 339
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 2 (d) 5
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 17 (c) 8 (d) 19
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11

Answer key

  1. 7
  2. 14
  3. 6
  4. 201
  5. 486
  6. 4
  7. 4
  8. 45
  9. 618
  10. 57
  11. 19
  12. 7
  13. 3
  14. 18
  15. 19
  16. 5
  17. 48
  18. 79
  19. 3
  20. 507
  21. 5
  22. 27
  23. 69
  24. 9
  25. 18
  26. 8
  27. 18
  28. 4
  29. 30
  30. 15
  31. 17
  32. 2
  33. 246
  34. 54
  35. 7
  36. 339
  37. 4
  38. 18
  39. 18
  40. 9

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