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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 722 · 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 8 written when you write all the numbers from 1 to 83? (a) 13 (b) 10 (c) 12 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  3. 3.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) 10 (b) 30 (c) 90 (d) 33
  4. 4.The numbers 1 to 9 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) 5 (c) 45 (d) 15
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 4 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  8. 8.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) 162 (c) 18 (d) 57
  9. 9.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 418 (c) 520 (d) 519
  10. 10.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
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 14 (b) 8 (c) 13 (d) 11
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  13. 13.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 148 (c) 158 (d) 157
  14. 14.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 501 (d) 406
  15. 15.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) 153 (b) 51 (c) 17 (d) 54
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  17. 17.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) 9 (b) 81 (c) 30 (d) 27
  18. 18.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 312 (c) 360 (d) 361
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 8 (b) 10 (c) 9 (d) 11
  20. 20.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 630 (c) 639 (d) 498
  21. 21.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) 63 (b) 189 (c) 66 (d) 21
  22. 22.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 556 (c) 555 (d) 546
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 13 (c) 3 (d) 14
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 18 (d) 16
  25. 25.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 120 (c) 112 (d) 102
  26. 26.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 339 (c) 349 (d) 304
  27. 27.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 217 (c) 216 (d) 324
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 16 (d) 5
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 3 (d) 2
  30. 30.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) 24 (b) 72 (c) 27 (d) 8
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 8 (c) 9 (d) 3
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 14 (b) 13 (c) 4 (d) 15
  34. 34.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) 42 (d) 126
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 19 (d) 8
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  37. 37.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 5 (c) 4 (d) 2
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 15 (b) 13 (c) 14 (d) 5
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 2 (d) 5

Answer key

  1. 12
  2. 3
  3. 30
  4. 15
  5. 5
  6. 5
  7. 9
  8. 54
  9. 519
  10. 21
  11. 13
  12. 5
  13. 157
  14. 501
  15. 51
  16. 4
  17. 27
  18. 360
  19. 10
  20. 639
  21. 63
  22. 555
  23. 13
  24. 17
  25. 111
  26. 348
  27. 216
  28. 16
  29. 3
  30. 24
  31. 6
  32. 9
  33. 14
  34. 42
  35. 18
  36. 18
  37. 8
  38. 4
  39. 14
  40. 4

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