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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 499 · 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 10? (a) 10 (b) 8 (c) 9 (d) 11
  2. 2.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) 6 (b) 18 (c) 21 (d) 54
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 14 (d) 15
  4. 4.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) 11 (b) 99 (c) 36 (d) 33
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 5 (d) 17
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  10. 10.The numbers 6 to 14 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) 10 (c) 33 (d) 90
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 17 (d) 15
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  13. 13.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 144 (c) 152 (d) 143
  14. 14.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  16. 16.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) 108 (c) 39 (d) 36
  17. 17.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) 27 (c) 81 (d) 9
  18. 18.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
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 6 (d) 5
  20. 20.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) 14 (c) 126 (d) 42
  21. 21.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 72 (d) 8
  22. 22.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) 21 (c) 189 (d) 63
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 15 (d) 17
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 18 (b) 19 (c) 20 (d) 9
  25. 25.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 184 (c) 166 (d) 175
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 4 (c) 16 (d) 15
  27. 27.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 538 (c) 528 (d) 537
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 19 (d) 21
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 19 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  34. 34.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 601 (d) 600
  35. 35.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 586 (c) 576 (d) 585
  36. 36.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 360 (c) 351 (d) 361
  37. 37.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 80 (c) 89 (d) 90
  38. 38.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 173 (c) 174 (d) 182
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 8 (d) 19
  40. 40.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

Answer key

  1. 9
  2. 18
  3. 15
  4. 33
  5. 7
  6. 16
  7. 4
  8. 19
  9. 2
  10. 30
  11. 16
  12. 4
  13. 143
  14. 81
  15. 17
  16. 36
  17. 27
  18. 69
  19. 5
  20. 42
  21. 24
  22. 63
  23. 16
  24. 19
  25. 175
  26. 15
  27. 537
  28. 3
  29. 17
  30. 8
  31. 20
  32. 18
  33. 6
  34. 600
  35. 585
  36. 360
  37. 89
  38. 173
  39. 19
  40. 4

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