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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 456 · 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.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) 14 (b) 42 (c) 126 (d) 45
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  4. 4.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 183 (c) 192 (d) 184
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  6. 6.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 46 (c) 37 (d) 28
  7. 7.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 346 (c) 336 (d) 302
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 21 (d) 9
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 2 (c) 4 (d) 3
  10. 10.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) 33 (b) 36 (c) 11 (d) 99
  11. 11.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 198 (c) 204 (d) 189
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  14. 14.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) 12 (b) 39 (c) 108 (d) 36
  15. 15.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 267 (c) 256 (d) 276
  16. 16.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) 60 (b) 20 (c) 63 (d) 180
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 3 (c) 5 (d) 6
  18. 18.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 54 (d) 36
  19. 19.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) 54 (b) 153 (c) 51 (d) 17
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 8 (c) 18 (d) 19
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 6 (b) 5 (c) 8 (d) 7
  23. 23.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) 171 (c) 57 (d) 60
  24. 24.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 615 (c) 482 (d) 606
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  26. 26.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 618 (c) 490 (d) 628
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 7 (c) 5 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 16 (d) 7
  31. 31.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) 9 (b) 81 (c) 30 (d) 27
  32. 32.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 136 (c) 144 (d) 135
  33. 33.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) 21 (b) 18 (c) 6 (d) 54
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  36. 36.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 59 (c) 50 (d) 60
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 1 (d) 2
  39. 39.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) 18 (d) 15
  40. 40.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 49 (c) 40 (d) 58

Answer key

  1. 42
  2. 6
  3. 9
  4. 183
  5. 7
  6. 37
  7. 345
  8. 20
  9. 4
  10. 33
  11. 198
  12. 18
  13. 8
  14. 36
  15. 276
  16. 60
  17. 5
  18. 45
  19. 51
  20. 19
  21. 4
  22. 7
  23. 57
  24. 615
  25. 2
  26. 627
  27. 6
  28. 2
  29. 7
  30. 17
  31. 27
  32. 135
  33. 18
  34. 3
  35. 15
  36. 59
  37. 9
  38. 3
  39. 15
  40. 49

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