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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 733 · 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 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
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  3. 3.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 387 (c) 336 (d) 397
  4. 4.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) 126 (b) 14 (c) 45 (d) 42
  5. 5.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) 164 (c) 174 (d) 173
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 18 (d) 19
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 6 (c) 7 (d) 5
  9. 9.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 222 (d) 226
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 17 (d) 6
  11. 11.The numbers 11 to 19 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) 48 (c) 45 (d) 135
  12. 12.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 64 (c) 73 (d) 82
  13. 13.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 94 (d) 102
  14. 14.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 116 (c) 98 (d) 108
  15. 15.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) 180 (b) 20 (c) 60 (d) 63
  16. 16.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) 63 (b) 21 (c) 24 (d) 7
  17. 17.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 196 (c) 195 (d) 202
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  19. 19.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) 39 (c) 36 (d) 12
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  21. 21.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 597 (c) 598 (d) 588
  22. 22.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) 27 (b) 30 (c) 81 (d) 9
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 5 (c) 6 (d) 7
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 17 (c) 6 (d) 16
  26. 26.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 231 (c) 232 (d) 240
  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) 120 (b) 111 (c) 112 (d) 102
  28. 28.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) 24 (b) 72 (c) 75 (d) 216
  29. 29.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 86 (c) 104 (d) 95
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 7 (c) 8 (d) 5
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  32. 32.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 492 (c) 406 (d) 501
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 11 (b) 13 (c) 4 (d) 12
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 16 (b) 4 (c) 15 (d) 14
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 4 (c) 5 (d) 6
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  38. 38.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 274 (c) 304 (d) 294
  39. 39.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) 36 (b) 99 (c) 33 (d) 11
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 19 (d) 18

Answer key

  1. 18
  2. 3
  3. 396
  4. 42
  5. 173
  6. 8
  7. 19
  8. 6
  9. 231
  10. 17
  11. 45
  12. 73
  13. 93
  14. 107
  15. 60
  16. 21
  17. 195
  18. 9
  19. 36
  20. 7
  21. 597
  22. 27
  23. 6
  24. 3
  25. 16
  26. 240
  27. 111
  28. 72
  29. 95
  30. 7
  31. 2
  32. 501
  33. 12
  34. 7
  35. 15
  36. 5
  37. 4
  38. 303
  39. 33
  40. 19

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