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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 285 · 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.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) 15 (c) 5 (d) 45
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  3. 3.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) 39 (c) 117 (d) 42
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 21 (d) 9
  5. 5.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
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  9. 9.The numbers 4 to 12 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) 72 (c) 8 (d) 27
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  11. 11.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) 36 (d) 11
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  13. 13.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 84 (d) 83
  14. 14.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 304 (c) 303 (d) 294
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  16. 16.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 482 (c) 606 (d) 615
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 18
  18. 18.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 54 (d) 46
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 4 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  21. 21.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 72 (c) 64 (d) 54
  22. 22.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 465 (c) 382 (d) 456
  23. 23.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) 486 (c) 487 (d) 477
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 17 (b) 15 (c) 6 (d) 16
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 6 (c) 5 (d) 4
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 14 (d) 4
  28. 28.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) 619 (c) 484 (d) 618
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  30. 30.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 268 (c) 294 (d) 295
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 19 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  33. 33.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 498 (c) 508 (d) 507
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 13 (c) 4 (d) 14
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 6 (d) 3
  38. 38.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) 48 (b) 144 (c) 16 (d) 51
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17

Answer key

  1. 15
  2. 7
  3. 39
  4. 20
  5. 21
  6. 19
  7. 6
  8. 8
  9. 24
  10. 7
  11. 33
  12. 9
  13. 83
  14. 303
  15. 5
  16. 615
  17. 19
  18. 45
  19. 6
  20. 5
  21. 63
  22. 465
  23. 486
  24. 4
  25. 16
  26. 5
  27. 14
  28. 618
  29. 16
  30. 294
  31. 18
  32. 2
  33. 507
  34. 13
  35. 9
  36. 8
  37. 5
  38. 48
  39. 19
  40. 3

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