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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 958 · 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.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 74 (d) 84
  2. 2.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) 493 (c) 492 (d) 400
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  5. 5.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) 11 (b) 36 (c) 99 (d) 33
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 10 (b) 12 (c) 13 (d) 9
  8. 8.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) 30 (c) 27 (d) 9
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  10. 10.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
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  13. 13.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 201 (c) 192 (d) 202
  14. 14.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) 57 (b) 162 (c) 54 (d) 18
  15. 15.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 26 (d) 35
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 3 (d) 4
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 3 (d) 4
  18. 18.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) 107 (c) 98 (d) 108
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 14 (c) 13 (d) 3
  22. 22.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 423 (c) 433 (d) 432
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 17 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  25. 25.The numbers 17 to 25 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) 66 (c) 189 (d) 21
  26. 26.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 12 (d) 108
  27. 27.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 48 (c) 40 (d) 30
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  29. 29.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 452 (c) 570 (d) 571
  30. 30.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 92 (d) 110
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 15 (d) 4
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 17
  33. 33.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) 42 (b) 45 (c) 126 (d) 14
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  38. 38.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 246 (c) 252 (d) 261
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  40. 40.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) 18 (b) 54 (c) 21 (d) 6

Answer key

  1. 83
  2. 492
  3. 4
  4. 2
  5. 33
  6. 9
  7. 12
  8. 27
  9. 8
  10. 30
  11. 4
  12. 5
  13. 201
  14. 54
  15. 35
  16. 5
  17. 3
  18. 107
  19. 18
  20. 7
  21. 14
  22. 432
  23. 17
  24. 7
  25. 63
  26. 36
  27. 39
  28. 3
  29. 570
  30. 101
  31. 15
  32. 16
  33. 42
  34. 9
  35. 3
  36. 18
  37. 17
  38. 261
  39. 6
  40. 18

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