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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 993 · 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 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) 135 (b) 45 (c) 48 (d) 15
  2. 2.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) 36 (c) 26 (d) 44
  3. 3.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 412 (c) 511 (d) 501
  4. 4.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 282 (c) 283 (d) 260
  5. 5.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) 99 (b) 11 (c) 36 (d) 33
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 20 (d) 19
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 17
  8. 8.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) 27 (c) 8 (d) 24
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  10. 10.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) 48 (b) 51 (c) 16 (d) 144
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  12. 12.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 225 (c) 226 (d) 216
  13. 13.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 135 (c) 126 (d) 136
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 20 (d) 19
  18. 18.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 171 (d) 19
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 9 (d) 20
  20. 20.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) 36 (c) 12 (d) 39
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 14 (d) 13
  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) 189 (b) 21 (c) 63 (d) 66
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  24. 24.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 448 (c) 438 (d) 370
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
  26. 26.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 394 (c) 474 (d) 484
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  28. 28.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) 126 (c) 42 (d) 45
  29. 29.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) 207 (c) 23 (d) 69
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 13 (c) 14 (d) 4
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 5 (c) 7 (d) 4
  33. 33.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 158 (c) 176 (d) 168
  34. 34.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 165 (d) 166
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  36. 36.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 294 (c) 333 (d) 334
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  38. 38.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) 33 (c) 90 (d) 10
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  40. 40.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 54 (d) 18

Answer key

  1. 45
  2. 35
  3. 510
  4. 282
  5. 33
  6. 19
  7. 18
  8. 24
  9. 7
  10. 48
  11. 5
  12. 225
  13. 135
  14. 9
  15. 9
  16. 7
  17. 19
  18. 57
  19. 19
  20. 36
  21. 14
  22. 63
  23. 4
  24. 447
  25. 18
  26. 483
  27. 5
  28. 42
  29. 69
  30. 3
  31. 14
  32. 7
  33. 167
  34. 165
  35. 2
  36. 333
  37. 6
  38. 30
  39. 4
  40. 54

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