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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 575 · 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.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 4 (c) 5 (d) 3
  2. 2.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) 9 (c) 30 (d) 27
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 14 (d) 13
  6. 6.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) 13 (c) 42 (d) 39
  7. 7.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) 173 (d) 164
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 5 (b) 3 (c) 6 (d) 4
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
  10. 10.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 155 (d) 164
  11. 11.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 78 (d) 77
  12. 12.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 36 (d) 35
  13. 13.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 315 (c) 282 (d) 316
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  15. 15.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) 18 (d) 54
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19
  18. 18.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) 24 (d) 8
  19. 19.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 291 (c) 266 (d) 282
  20. 20.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 357 (d) 358
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 16 (d) 18
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 1 (d) 2
  23. 23.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 633 (c) 642 (d) 643
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 18 (d) 19
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 3 (c) 15 (d) 14
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 6 (d) 4
  27. 27.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) 90 (c) 10 (d) 33
  28. 28.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 264 (c) 288 (d) 279
  29. 29.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  30. 30.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
  31. 31.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 372 (c) 441 (d) 450
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 7 (d) 17
  33. 33.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) 14 (c) 126 (d) 42
  34. 34.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 466 (c) 456 (d) 382
  35. 35.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
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 18 (d) 17
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 19 (d) 7
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 9 (d) 20
  40. 40.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) 66 (c) 21 (d) 63

Answer key

  1. 4
  2. 27
  3. 8
  4. 6
  5. 14
  6. 39
  7. 173
  8. 5
  9. 20
  10. 155
  11. 77
  12. 35
  13. 315
  14. 2
  15. 54
  16. 5
  17. 19
  18. 24
  19. 291
  20. 357
  21. 17
  22. 3
  23. 642
  24. 18
  25. 14
  26. 5
  27. 30
  28. 288
  29. 9
  30. 4
  31. 450
  32. 18
  33. 42
  34. 465
  35. 36
  36. 18
  37. 18
  38. 16
  39. 20
  40. 63

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