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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 80 · 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 60? (a) 15 (b) 16 (c) 6 (d) 17
  2. 2.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) 63 (c) 20 (d) 60
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 3 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  8. 8.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 550 (c) 549 (d) 438
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 2 (d) 4
  10. 10.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 61 (c) 70 (d) 52
  11. 11.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) 81 (b) 27 (c) 30 (d) 9
  12. 12.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 482 (b) 616 (c) 606 (d) 615
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  14. 14.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 402 (c) 403 (d) 393
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 3 (c) 2 (d) 1
  16. 16.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 46 (c) 55 (d) 56
  17. 17.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 326 (d) 381
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 17 (d) 18
  19. 19.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) 46 (c) 45 (d) 54
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 20
  22. 22.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 579 (d) 458
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  24. 24.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 92 (c) 100 (d) 82
  25. 25.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) 33 (c) 90 (d) 10
  26. 26.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 406 (c) 396 (d) 405
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  28. 28.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
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 6 (d) 17
  30. 30.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) 69 (d) 207
  31. 31.The numbers 20 to 28 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) 75 (c) 216 (d) 24
  32. 32.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 40 (d) 58
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 11 (b) 13 (c) 4 (d) 12
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 2 (c) 3 (d) 4
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 18 (d) 16
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 13 (d) 12
  39. 39.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) 21 (c) 24 (d) 7
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 8 (b) 7 (c) 6 (d) 5

Answer key

  1. 16
  2. 60
  3. 3
  4. 6
  5. 5
  6. 4
  7. 18
  8. 549
  9. 4
  10. 61
  11. 27
  12. 615
  13. 5
  14. 402
  15. 3
  16. 55
  17. 381
  18. 18
  19. 45
  20. 6
  21. 19
  22. 579
  23. 17
  24. 91
  25. 30
  26. 405
  27. 9
  28. 15
  29. 17
  30. 69
  31. 72
  32. 49
  33. 9
  34. 12
  35. 2
  36. 4
  37. 17
  38. 13
  39. 21
  40. 7

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