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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 405 · 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 two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  2. 2.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 184 (c) 166 (d) 175
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  4. 4.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 516 (c) 422 (d) 525
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 16 (c) 5 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  7. 7.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) 63 (b) 7 (c) 24 (d) 21
  8. 8.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) 21 (b) 189 (c) 66 (d) 63
  9. 9.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) 5 (b) 45 (c) 18 (d) 15
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 15 (b) 14 (c) 5 (d) 16
  11. 11.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 564 (c) 555 (d) 565
  12. 12.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 162 (c) 152 (d) 170
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 14 (c) 13 (d) 15
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  16. 16.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) 99 (b) 36 (c) 11 (d) 33
  17. 17.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
  18. 18.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 26 (d) 35
  19. 19.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) 16 (b) 144 (c) 48 (d) 51
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 12 (c) 13 (d) 11
  21. 21.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 585 (c) 468 (d) 595
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 16 (b) 7 (c) 17 (d) 18
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 3 (d) 4
  25. 25.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) 13 (b) 117 (c) 39 (d) 42
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 13 (b) 12 (c) 3 (d) 14
  28. 28.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 59 (c) 60 (d) 50
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 4 (d) 5
  30. 30.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 486 (d) 402
  31. 31.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) 90 (c) 30 (d) 33
  32. 32.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) 23 (b) 69 (c) 207 (d) 72
  33. 33.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
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 21 (d) 9
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 9 (d) 18
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 7 (c) 6 (d) 5
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 5 (d) 4
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  39. 39.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 423 (c) 424 (d) 354
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 16 (d) 4

Answer key

  1. 9
  2. 175
  3. 7
  4. 525
  5. 16
  6. 3
  7. 21
  8. 63
  9. 15
  10. 15
  11. 564
  12. 161
  13. 5
  14. 14
  15. 9
  16. 33
  17. 24
  18. 35
  19. 48
  20. 12
  21. 594
  22. 3
  23. 17
  24. 3
  25. 39
  26. 6
  27. 13
  28. 59
  29. 4
  30. 495
  31. 30
  32. 69
  33. 54
  34. 20
  35. 19
  36. 6
  37. 5
  38. 2
  39. 423
  40. 15

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