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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 800 · 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 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) 75 (b) 24 (c) 72 (d) 216
  2. 2.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 424 (c) 529 (d) 528
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 16 (c) 14 (d) 15
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 8 (d) 17
  5. 5.The numbers 13 to 21 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) 153 (c) 51 (d) 17
  6. 6.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
  7. 7.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
  8. 8.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) 30 (c) 33 (d) 10
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 5 (b) 7 (c) 10 (d) 9
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 18 (b) 7 (c) 17 (d) 16
  11. 11.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) 57 (b) 162 (c) 54 (d) 18
  12. 12.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) 18 (b) 6 (c) 54 (d) 21
  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) 171 (b) 60 (c) 19 (d) 57
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 13 (d) 4
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  16. 16.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) 39 (c) 42 (d) 13
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  18. 18.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) 16 (c) 144 (d) 51
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 9 (d) 20
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 20 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 20
  23. 23.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
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
  25. 25.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) 67 (c) 58 (d) 76
  26. 26.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) 207 (b) 69 (c) 72 (d) 23
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 2 (d) 5
  28. 28.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 207 (c) 217 (d) 216
  29. 29.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) 33 (c) 11 (d) 99
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 18 (b) 9 (c) 17 (d) 15
  31. 31.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 465 (c) 388 (d) 474
  32. 32.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 280 (c) 279 (d) 258
  33. 33.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) 22 (b) 198 (c) 66 (d) 69
  34. 34.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
  35. 35.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 442 (c) 366 (d) 432
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 15 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 8 (d) 17
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 5 (d) 14
  40. 40.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) 36 (c) 108 (d) 12

Answer key

  1. 72
  2. 528
  3. 15
  4. 18
  5. 51
  6. 157
  7. 282
  8. 30
  9. 9
  10. 17
  11. 54
  12. 18
  13. 57
  14. 14
  15. 8
  16. 39
  17. 9
  18. 48
  19. 19
  20. 19
  21. 9
  22. 19
  23. 173
  24. 18
  25. 67
  26. 69
  27. 4
  28. 216
  29. 33
  30. 17
  31. 474
  32. 279
  33. 66
  34. 53
  35. 441
  36. 15
  37. 3
  38. 18
  39. 15
  40. 36

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