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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 73 · 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) 18 (d) 5
  2. 2.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) 108 (b) 12 (c) 36 (d) 39
  3. 3.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 7 (c) 21 (d) 63
  4. 4.The numbers 20 to 28 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) 24 (c) 75 (d) 216
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 14 (d) 16
  8. 8.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 155 (c) 146 (d) 156
  9. 9.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 44 (c) 26 (d) 36
  10. 10.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) 199 (c) 198 (d) 189
  11. 11.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
  12. 12.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 513 (c) 523 (d) 420
  13. 13.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
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 16 (b) 5 (c) 15 (d) 14
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 17 (b) 15 (c) 5 (d) 16
  17. 17.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 468 (c) 384 (d) 459
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 15 (c) 14 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 17 (d) 19
  21. 21.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 146 (c) 138 (d) 128
  22. 22.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 62 (d) 53
  23. 23.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 154 (c) 146 (d) 136
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 18 (d) 7
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 21 (d) 19
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 1 (b) 3 (c) 2 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  32. 32.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 190 (c) 180 (d) 189
  33. 33.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 174 (c) 164 (d) 173
  34. 34.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 122 (c) 140 (d) 131
  35. 35.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 94 (c) 93 (d) 102
  36. 36.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) 144 (c) 51 (d) 48
  37. 37.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 408 (c) 417 (d) 350
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 9 (c) 12 (d) 11
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7

Answer key

  1. 15
  2. 36
  3. 21
  4. 72
  5. 9
  6. 3
  7. 15
  8. 155
  9. 35
  10. 198
  11. 113
  12. 522
  13. 39
  14. 15
  15. 3
  16. 16
  17. 468
  18. 14
  19. 9
  20. 18
  21. 137
  22. 53
  23. 145
  24. 2
  25. 20
  26. 18
  27. 20
  28. 3
  29. 4
  30. 3
  31. 4
  32. 189
  33. 173
  34. 131
  35. 93
  36. 48
  37. 417
  38. 11
  39. 19
  40. 8

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