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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 412 · 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 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) 54 (b) 57 (c) 18 (d) 162
  2. 2.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 312 (c) 351 (d) 360
  3. 3.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 33 (d) 34
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 18 (d) 19
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 8 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 6 (c) 4 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  9. 9.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) 42 (c) 117 (d) 39
  10. 10.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 384 (c) 468 (d) 459
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 15 (b) 3 (c) 14 (d) 13
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  15. 15.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 452 (c) 561 (d) 571
  16. 16.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 246 (d) 262
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  19. 19.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 76 (c) 66 (d) 84
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 16 (c) 15 (d) 8
  22. 22.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 591 (c) 592 (d) 582
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 18 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 16 (d) 18
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 15 (d) 17
  28. 28.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 146 (c) 145 (d) 154
  29. 29.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 625 (d) 624
  30. 30.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) 22 (d) 198
  31. 31.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 54 (d) 72
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 5 (b) 6 (c) 7 (d) 4
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 8 (b) 6 (c) 7 (d) 5
  35. 35.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) 7 (b) 24 (c) 21 (d) 63
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 10 (c) 13 (d) 12
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  38. 38.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) 54 (c) 18 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  40. 40.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) 10 (c) 30 (d) 90

Answer key

  1. 54
  2. 360
  3. 33
  4. 19
  5. 19
  6. 9
  7. 6
  8. 6
  9. 39
  10. 468
  11. 3
  12. 14
  13. 8
  14. 2
  15. 570
  16. 261
  17. 7
  18. 2
  19. 75
  20. 15
  21. 15
  22. 591
  23. 17
  24. 9
  25. 5
  26. 17
  27. 16
  28. 145
  29. 624
  30. 66
  31. 63
  32. 4
  33. 6
  34. 7
  35. 21
  36. 12
  37. 8
  38. 18
  39. 6
  40. 30

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