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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 867 · 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 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  4. 4.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
  5. 5.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 54 (d) 51
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  9. 9.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 20 (b) 19 (c) 18 (d) 8
  11. 11.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) 72 (c) 63 (d) 54
  12. 12.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 51 (d) 52
  13. 13.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) 207 (b) 72 (c) 69 (d) 23
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  16. 16.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
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 17 (b) 15 (c) 5 (d) 16
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 4 (d) 5
  19. 19.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 56 (c) 48 (d) 47
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 11 (b) 9 (c) 10 (d) 12
  21. 21.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 120 (c) 129 (d) 138
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 7 (c) 5 (d) 6
  23. 23.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 603 (c) 604 (d) 594
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  25. 25.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 552 (c) 553 (d) 543
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 18 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  28. 28.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) 42 (b) 13 (c) 39 (d) 117
  29. 29.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) 12 (c) 36 (d) 108
  30. 30.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) 20 (c) 63 (d) 60
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 5 (d) 7
  32. 32.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 264 (c) 255 (d) 248
  33. 33.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 32 (d) 50
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  35. 35.The numbers 15 to 23 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) 19 (c) 171 (d) 57
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 7 (b) 5 (c) 4 (d) 8
  38. 38.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 132 (d) 122
  39. 39.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 160 (d) 159
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 7 (b) 6 (c) 8 (d) 5

Answer key

  1. 18
  2. 19
  3. 6
  4. 15
  5. 51
  6. 20
  7. 2
  8. 19
  9. 113
  10. 19
  11. 63
  12. 51
  13. 69
  14. 5
  15. 4
  16. 27
  17. 16
  18. 4
  19. 47
  20. 11
  21. 129
  22. 7
  23. 603
  24. 7
  25. 552
  26. 18
  27. 8
  28. 39
  29. 36
  30. 60
  31. 6
  32. 264
  33. 41
  34. 9
  35. 57
  36. 3
  37. 7
  38. 131
  39. 159
  40. 7

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