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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 145 · 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 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) 15 (b) 45 (c) 5 (d) 18
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 6 (b) 5 (c) 7 (d) 8
  4. 4.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 198 (d) 199
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  6. 6.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 570 (c) 561 (d) 452
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 17 (d) 18
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 2 (d) 5
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 13 (d) 15
  16. 16.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) 54 (c) 6 (d) 18
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 18 (b) 19 (c) 9 (d) 20
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  20. 20.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) 21 (b) 189 (c) 66 (d) 63
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 4 (d) 14
  22. 22.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 358 (c) 348 (d) 310
  23. 23.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 41 (c) 50 (d) 32
  24. 24.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 427 (c) 417 (d) 426
  25. 25.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 274 (c) 264 (d) 273
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 9 (d) 19
  27. 27.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) 23 (b) 72 (c) 207 (d) 69
  28. 28.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) 110 (d) 92
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 3 (c) 14 (d) 15
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 3 (d) 5
  32. 32.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) 45 (c) 126 (d) 42
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 5 (d) 3
  34. 34.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 338 (c) 390 (d) 399
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 15 (b) 13 (c) 14 (d) 5
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 19 (c) 20 (d) 9
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 6 (b) 7 (c) 5 (d) 8
  39. 39.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) 17 (d) 54
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1

Answer key

  1. 15
  2. 8
  3. 7
  4. 198
  5. 9
  6. 570
  7. 5
  8. 19
  9. 9
  10. 4
  11. 5
  12. 6
  13. 17
  14. 4
  15. 14
  16. 18
  17. 6
  18. 19
  19. 3
  20. 63
  21. 15
  22. 357
  23. 41
  24. 426
  25. 273
  26. 19
  27. 69
  28. 101
  29. 8
  30. 14
  31. 5
  32. 42
  33. 4
  34. 399
  35. 3
  36. 14
  37. 20
  38. 7
  39. 51
  40. 2

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