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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 481 · 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 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) 66 (c) 21 (d) 189
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  3. 3.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) 27 (b) 81 (c) 9 (d) 30
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  6. 6.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 526 (c) 525 (d) 422
  7. 7.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) 22 (b) 66 (c) 198 (d) 69
  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) 18 (b) 57 (c) 54 (d) 162
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  11. 11.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) 145 (c) 136 (d) 146
  12. 12.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 446 (c) 562 (d) 561
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 17 (b) 5 (c) 16 (d) 15
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 17 (d) 8
  15. 15.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 132 (d) 122
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  21. 21.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) 108 (c) 12 (d) 36
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 15 (b) 14 (c) 5 (d) 16
  26. 26.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) 72 (c) 23 (d) 207
  27. 27.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 267 (c) 268 (d) 250
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 4 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  30. 30.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 303 (c) 313 (d) 280
  31. 31.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 144 (c) 152 (d) 143
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 5 (b) 7 (c) 6 (d) 8
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 15 (b) 5 (c) 16 (d) 17
  34. 34.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
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 3 (b) 5 (c) 4 (d) 2
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 4 (d) 5
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 3 (d) 5
  39. 39.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) 6 (b) 18 (c) 54 (d) 21
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 5 (b) 7 (c) 6 (d) 4

Answer key

  1. 63
  2. 9
  3. 27
  4. 19
  5. 20
  6. 525
  7. 66
  8. 54
  9. 9
  10. 17
  11. 145
  12. 561
  13. 16
  14. 18
  15. 131
  16. 6
  17. 19
  18. 5
  19. 8
  20. 4
  21. 36
  22. 2
  23. 7
  24. 5
  25. 15
  26. 69
  27. 267
  28. 5
  29. 4
  30. 312
  31. 143
  32. 7
  33. 16
  34. 48
  35. 19
  36. 4
  37. 4
  38. 5
  39. 18
  40. 6

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