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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 163 · 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 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 182 (c) 181 (d) 190
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  4. 4.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 270 (d) 279
  5. 5.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 101 (c) 92 (d) 110
  6. 6.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) 66 (b) 189 (c) 63 (d) 21
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 16 (d) 6
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 15 (d) 3
  9. 9.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 155 (d) 164
  10. 10.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) 18 (c) 54 (d) 162
  11. 11.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) 144 (c) 48 (d) 16
  12. 12.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) 7 (d) 63
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 18 (d) 17
  14. 14.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 595 (d) 594
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  16. 16.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 170 (c) 169 (d) 160
  17. 17.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 69 (c) 78 (d) 70
  18. 18.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) 45 (b) 126 (c) 14 (d) 42
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 7 (c) 17 (d) 18
  22. 22.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 261 (d) 252
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 20 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  25. 25.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 202 (c) 195 (d) 196
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 5 (c) 6 (d) 7
  27. 27.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 49 (c) 58 (d) 50
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 13 (d) 3
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 7 (c) 8 (d) 5
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 16 (c) 15 (d) 14
  32. 32.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) 198 (b) 22 (c) 66 (d) 69
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 4 (d) 7
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 9 (d) 21
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 1 (d) 2
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 13 (b) 15 (c) 3 (d) 14
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  40. 40.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 225 (c) 226 (d) 222

Answer key

  1. 181
  2. 3
  3. 5
  4. 279
  5. 101
  6. 63
  7. 17
  8. 14
  9. 155
  10. 54
  11. 48
  12. 21
  13. 17
  14. 594
  15. 4
  16. 169
  17. 69
  18. 42
  19. 2
  20. 17
  21. 18
  22. 270
  23. 19
  24. 7
  25. 195
  26. 6
  27. 49
  28. 2
  29. 13
  30. 7
  31. 15
  32. 66
  33. 6
  34. 20
  35. 3
  36. 14
  37. 18
  38. 18
  39. 8
  40. 225

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