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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 687 · 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 two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 3 (b) 2 (c) 5 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 14 (d) 4
  5. 5.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) 30 (b) 81 (c) 9 (d) 27
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 6 (c) 3 (d) 4
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 3 (d) 4
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 6 (d) 5
  9. 9.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 157 (c) 166 (d) 148
  10. 10.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 196 (c) 195 (d) 186
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 17 (d) 18
  15. 15.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) 19 (b) 57 (c) 60 (d) 171
  16. 16.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 88 (c) 96 (d) 78
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 18 (c) 16 (d) 6
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 12 (b) 13 (c) 8 (d) 10
  21. 21.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 253 (c) 252 (d) 243
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  23. 23.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 125 (c) 116 (d) 134
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 13 (d) 12
  26. 26.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
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 5 (d) 3
  29. 29.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 534 (c) 544 (d) 543
  30. 30.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) 51 (c) 54 (d) 153
  31. 31.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) 69 (b) 207 (c) 72 (d) 23
  32. 32.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) 45 (b) 15 (c) 135 (d) 48
  33. 33.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 412 (c) 511 (d) 501
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 3 (d) 1
  36. 36.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 138 (c) 137 (d) 128
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 4 (d) 3
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 4 (d) 15
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 7 (c) 8 (d) 5
  40. 40.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) 63 (b) 20 (c) 180 (d) 60

Answer key

  1. 4
  2. 4
  3. 6
  4. 15
  5. 27
  6. 5
  7. 4
  8. 5
  9. 157
  10. 195
  11. 4
  12. 5
  13. 2
  14. 18
  15. 57
  16. 87
  17. 17
  18. 8
  19. 17
  20. 12
  21. 252
  22. 2
  23. 125
  24. 17
  25. 13
  26. 66
  27. 6
  28. 4
  29. 543
  30. 51
  31. 69
  32. 45
  33. 510
  34. 3
  35. 3
  36. 137
  37. 5
  38. 15
  39. 7
  40. 60

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