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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 517 · 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 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 5 (c) 3 (d) 2
  2. 2.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) 15 (c) 48 (d) 45
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 18 (d) 19
  4. 4.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 586 (c) 576 (d) 462
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  6. 6.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) 24 (b) 72 (c) 216 (d) 75
  7. 7.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 202 (c) 195 (d) 186
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  9. 9.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 460 (c) 459 (d) 450
  10. 10.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 380 (c) 453 (d) 463
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  14. 14.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) 21 (c) 63 (d) 7
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 6 (d) 18
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  17. 17.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 400 (c) 493 (d) 492
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 9 (d) 21
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  21. 21.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 140 (c) 139 (d) 148
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 21 (d) 20
  24. 24.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) 18 (c) 162 (d) 57
  25. 25.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) 9 (b) 27 (c) 81 (d) 30
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 21 (d) 9
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 14 (c) 13 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 6 (d) 5
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 3 (d) 4
  35. 35.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 60 (d) 59
  36. 36.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 532 (c) 531 (d) 522
  37. 37.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) 5 (c) 15 (d) 45
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 7 (b) 8 (c) 6 (d) 9
  39. 39.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 95 (c) 86 (d) 104
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 16 (c) 17 (d) 15

Answer key

  1. 4
  2. 45
  3. 18
  4. 585
  5. 5
  6. 72
  7. 195
  8. 6
  9. 459
  10. 462
  11. 8
  12. 3
  13. 2
  14. 21
  15. 17
  16. 7
  17. 492
  18. 5
  19. 20
  20. 16
  21. 139
  22. 9
  23. 20
  24. 54
  25. 27
  26. 20
  27. 14
  28. 3
  29. 6
  30. 5
  31. 17
  32. 2
  33. 8
  34. 3
  35. 59
  36. 531
  37. 15
  38. 8
  39. 95
  40. 16

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