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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 599 · 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 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) 16 (b) 48 (c) 51 (d) 144
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  5. 5.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) 81 (c) 27 (d) 9
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 16
  7. 7.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) 72 (b) 8 (c) 27 (d) 24
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 15 (d) 4
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 3 (d) 5
  10. 10.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 58 (c) 67 (d) 76
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
  12. 12.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) 72 (b) 23 (c) 69 (d) 207
  13. 13.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) 66 (b) 69 (c) 198 (d) 22
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  16. 16.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 47 (c) 48 (d) 38
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 15 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 19 (d) 8
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 15 (c) 14 (d) 4
  21. 21.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 144 (c) 154 (d) 153
  22. 22.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 160 (c) 168 (d) 159
  23. 23.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) 36 (b) 12 (c) 108 (d) 39
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  25. 25.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) 10 (b) 90 (c) 33 (d) 30
  26. 26.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 217 (d) 216
  27. 27.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 112 (c) 120 (d) 111
  28. 28.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 134 (c) 143 (d) 144
  29. 29.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) 117 (b) 42 (c) 39 (d) 13
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 17 (d) 6
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 5 (d) 7
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 16 (d) 17
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 20 (b) 19 (c) 18 (d) 8
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 21 (d) 9
  37. 37.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 151 (c) 142 (d) 152
  38. 38.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 636 (c) 496 (d) 627
  39. 39.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) 90 (d) 89
  40. 40.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) 63 (c) 21 (d) 189

Answer key

  1. 48
  2. 3
  3. 4
  4. 2
  5. 27
  6. 15
  7. 24
  8. 15
  9. 5
  10. 67
  11. 3
  12. 69
  13. 66
  14. 18
  15. 5
  16. 47
  17. 15
  18. 7
  19. 19
  20. 15
  21. 153
  22. 159
  23. 36
  24. 9
  25. 30
  26. 216
  27. 111
  28. 143
  29. 39
  30. 8
  31. 4
  32. 17
  33. 6
  34. 17
  35. 19
  36. 20
  37. 151
  38. 636
  39. 89
  40. 63

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