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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 542 · 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 3? (a) 3 (b) 4 (c) 10 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  3. 3.The numbers 11 to 19 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) 135 (c) 45 (d) 48
  4. 4.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) 10 (c) 90 (d) 33
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 13 (d) 4
  6. 6.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) 66 (b) 21 (c) 63 (d) 189
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 17 (c) 8 (d) 18
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 2 (b) 1 (c) 4 (d) 3
  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) 15 (b) 45 (c) 5 (d) 18
  10. 10.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 52 (c) 34 (d) 43
  11. 11.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) 282 (c) 266 (d) 291
  12. 12.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) 39 (c) 42 (d) 117
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 6 (c) 7 (d) 9
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  15. 15.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 526 (c) 516 (d) 422
  16. 16.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) 24 (c) 7 (d) 21
  17. 17.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 94 (c) 86 (d) 76
  18. 18.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) 60 (b) 57 (c) 171 (d) 19
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  21. 21.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 96 (c) 104 (d) 86
  22. 22.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) 12 (c) 108 (d) 36
  23. 23.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 70 (d) 62
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 6 (d) 5
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 17 (b) 16 (c) 8 (d) 14
  26. 26.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  30. 30.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 146 (c) 136 (d) 145
  31. 31.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 519 (c) 529 (d) 528
  32. 32.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) 66 (b) 22 (c) 69 (d) 198
  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) 126 (b) 14 (c) 42 (d) 45
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 2 (d) 1
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 6 (b) 9 (c) 8 (d) 7
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 8 (b) 9 (c) 6 (d) 7
  39. 39.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 318 (d) 328
  40. 40.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) 11 (b) 36 (c) 33 (d) 99

Answer key

  1. 3
  2. 7
  3. 45
  4. 30
  5. 14
  6. 63
  7. 18
  8. 3
  9. 15
  10. 43
  11. 291
  12. 39
  13. 9
  14. 20
  15. 525
  16. 21
  17. 85
  18. 57
  19. 9
  20. 3
  21. 95
  22. 36
  23. 61
  24. 5
  25. 16
  26. 207
  27. 2
  28. 4
  29. 20
  30. 145
  31. 528
  32. 66
  33. 42
  34. 4
  35. 3
  36. 18
  37. 8
  38. 8
  39. 327
  40. 33

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