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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 510 · 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 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 18 (c) 17 (d) 16
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 12 (b) 14 (c) 15 (d) 8
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  4. 4.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 642 (c) 633 (d) 500
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 5 (c) 6 (d) 3
  9. 9.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 108 (c) 107 (d) 98
  10. 10.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 91 (c) 100 (d) 82
  11. 11.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 364 (c) 314 (d) 363
  12. 12.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 104 (c) 113 (d) 114
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 8 (b) 5 (c) 7 (d) 6
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 18 (d) 19
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  19. 19.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) 9 (c) 81 (d) 30
  20. 20.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 260 (c) 273 (d) 282
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  22. 22.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 348 (c) 339 (d) 304
  23. 23.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 559 (c) 549 (d) 444
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 18 (d) 19
  25. 25.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 175 (d) 176
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 6 (d) 17
  27. 27.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) 63 (d) 21
  28. 28.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) 60 (b) 20 (c) 63 (d) 180
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 15 (d) 17
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 5 (b) 16 (c) 15 (d) 14
  32. 32.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) 144 (d) 48
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 8 (d) 18
  34. 34.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 424 (c) 423 (d) 414
  35. 35.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) 10 (d) 90
  36. 36.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) 72 (b) 8 (c) 27 (d) 24
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  40. 40.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 45 (d) 42

Answer key

  1. 17
  2. 14
  3. 9
  4. 642
  5. 19
  6. 3
  7. 4
  8. 5
  9. 107
  10. 91
  11. 363
  12. 113
  13. 7
  14. 18
  15. 5
  16. 5
  17. 20
  18. 7
  19. 27
  20. 282
  21. 9
  22. 348
  23. 558
  24. 19
  25. 175
  26. 17
  27. 21
  28. 60
  29. 16
  30. 2
  31. 15
  32. 48
  33. 19
  34. 423
  35. 30
  36. 24
  37. 6
  38. 17
  39. 6
  40. 42

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