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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 166 · 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 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
  2. 2.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 453 (c) 444 (d) 374
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 8 (b) 10 (c) 5 (d) 11
  4. 4.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 292 (c) 321 (d) 330
  5. 5.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) 54 (c) 21 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  7. 7.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) 60 (c) 63 (d) 20
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  10. 10.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 116 (c) 125 (d) 134
  11. 11.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 561 (c) 571 (d) 570
  12. 12.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) 17 (d) 51
  13. 13.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 619 (c) 484 (d) 609
  14. 14.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) 51 (b) 144 (c) 48 (d) 16
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  16. 16.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 343 (c) 342 (d) 300
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 16 (b) 15 (c) 6 (d) 17
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 15 (d) 5
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 4 (d) 5
  23. 23.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) 33 (b) 90 (c) 30 (d) 10
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 4 (d) 15
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 9 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  30. 30.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) 63 (c) 66 (d) 21
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 4 (b) 5 (c) 7 (d) 6
  33. 33.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 333 (c) 324 (d) 334
  34. 34.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 154 (c) 162 (d) 153
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  36. 36.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) 8 (b) 27 (c) 24 (d) 72
  37. 37.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) 15 (b) 5 (c) 18 (d) 45
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 1
  39. 39.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) 69 (b) 207 (c) 23 (d) 72
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 5 (d) 6

Answer key

  1. 54
  2. 453
  3. 10
  4. 330
  5. 18
  6. 3
  7. 60
  8. 3
  9. 6
  10. 125
  11. 570
  12. 51
  13. 618
  14. 48
  15. 3
  16. 342
  17. 16
  18. 6
  19. 4
  20. 2
  21. 15
  22. 4
  23. 30
  24. 15
  25. 19
  26. 9
  27. 8
  28. 4
  29. 18
  30. 63
  31. 7
  32. 6
  33. 333
  34. 153
  35. 9
  36. 24
  37. 15
  38. 3
  39. 69
  40. 5

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