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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 625 · 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 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 134 (d) 143
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 6 (c) 5 (d) 4
  5. 5.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 352 (c) 420 (d) 411
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 6 (b) 5 (c) 7 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  8. 8.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 91 (d) 82
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 16 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 6 (b) 7 (c) 9 (d) 8
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  13. 13.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) 9 (c) 27 (d) 81
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 20 (d) 19
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  18. 18.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) 39 (c) 13 (d) 117
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 2 (d) 4
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 7 (b) 18 (c) 19 (d) 17
  22. 22.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 258 (c) 267 (d) 250
  23. 23.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 228 (c) 235 (d) 225
  24. 24.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 196 (c) 178 (d) 187
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 18 (d) 20
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 15 (c) 14 (d) 13
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 2 (d) 4
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 20 (d) 19
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  32. 32.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) 243 (d) 252
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 7 (d) 17
  34. 34.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) 45 (b) 5 (c) 15 (d) 18
  35. 35.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 66 (c) 74 (d) 65
  36. 36.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 199 (c) 198 (d) 204
  37. 37.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) 22 (b) 66 (c) 198 (d) 69
  38. 38.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) 51 (b) 153 (c) 54 (d) 17
  39. 39.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 474 (d) 484
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8

Answer key

  1. 143
  2. 6
  3. 2
  4. 6
  5. 420
  6. 6
  7. 5
  8. 91
  9. 17
  10. 4
  11. 8
  12. 3
  13. 27
  14. 2
  15. 4
  16. 19
  17. 4
  18. 39
  19. 3
  20. 3
  21. 18
  22. 267
  23. 234
  24. 187
  25. 9
  26. 8
  27. 19
  28. 14
  29. 4
  30. 20
  31. 5
  32. 252
  33. 18
  34. 15
  35. 65
  36. 198
  37. 66
  38. 51
  39. 483
  40. 18

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