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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 223 · 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 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) 81 (b) 27 (c) 30 (d) 9
  2. 2.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) 7 (b) 63 (c) 21 (d) 24
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 3 (d) 5
  4. 4.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) 54 (b) 18 (c) 162 (d) 57
  5. 5.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 49 (c) 50 (d) 40
  6. 6.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) 63 (d) 60
  7. 7.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 210 (c) 211 (d) 212
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  9. 9.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 396 (c) 387 (d) 397
  10. 10.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) 126 (c) 42 (d) 14
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 4 (c) 7 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  13. 13.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) 19 (b) 60 (c) 171 (d) 57
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 4 (b) 6 (c) 5 (d) 7
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 4 (b) 12 (c) 14 (d) 13
  16. 16.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 177 (c) 168 (d) 186
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  18. 18.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 106 (c) 114 (d) 105
  19. 19.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) 33 (d) 36
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 16 (c) 15 (d) 17
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 14 (c) 15 (d) 13
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  24. 24.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) 39 (b) 12 (c) 36 (d) 108
  25. 25.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
  26. 26.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 57 (c) 66 (d) 58
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 1
  28. 28.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 204 (c) 199 (d) 189
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 7 (b) 4 (c) 5 (d) 6
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  32. 32.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) 90 (b) 33 (c) 10 (d) 30
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  34. 34.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 576 (c) 567 (d) 456
  35. 35.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  36. 36.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 296 (c) 327 (d) 337
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 17 (d) 15
  38. 38.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 7 (b) 19 (c) 18 (d) 17
  40. 40.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 579 (c) 458 (d) 580

Answer key

  1. 27
  2. 21
  3. 4
  4. 54
  5. 49
  6. 60
  7. 210
  8. 5
  9. 396
  10. 42
  11. 6
  12. 9
  13. 57
  14. 6
  15. 13
  16. 177
  17. 5
  18. 105
  19. 33
  20. 3
  21. 16
  22. 14
  23. 4
  24. 36
  25. 24
  26. 57
  27. 3
  28. 198
  29. 3
  30. 6
  31. 9
  32. 30
  33. 2
  34. 576
  35. 6
  36. 336
  37. 16
  38. 7
  39. 18
  40. 579

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