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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 777 · 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.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 72 (d) 81
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  3. 3.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) 21 (d) 66
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  5. 5.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) 99 (d) 33
  6. 6.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) 30 (d) 9
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  9. 9.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 154 (c) 145 (d) 146
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 20 (d) 18
  11. 11.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) 57 (c) 162 (d) 18
  12. 12.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 62 (c) 70 (d) 52
  13. 13.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 258 (c) 270 (d) 279
  14. 14.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) 19 (c) 57 (d) 171
  15. 15.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 314 (c) 364 (d) 354
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  17. 17.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 124 (c) 114 (d) 123
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  21. 21.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) 21 (b) 6 (c) 18 (d) 54
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 17 (d) 19
  24. 24.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 321 (c) 214 (d) 213
  25. 25.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) 207 (b) 23 (c) 72 (d) 69
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 17 (b) 16 (c) 7 (d) 18
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 16 (b) 7 (c) 17 (d) 18
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 21 (c) 19 (d) 9
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 4 (d) 16
  31. 31.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) 20 (b) 60 (c) 63 (d) 180
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 19 (d) 18
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  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) 48 (b) 16 (c) 144 (d) 51
  35. 35.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 24 (d) 75
  36. 36.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 312 (c) 280 (d) 313
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 4 (c) 9 (d) 6
  38. 38.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) 17 (b) 153 (c) 51 (d) 54
  39. 39.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 382 (c) 456 (d) 466
  40. 40.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

Answer key

  1. 81
  2. 4
  3. 63
  4. 5
  5. 33
  6. 27
  7. 5
  8. 3
  9. 145
  10. 19
  11. 54
  12. 61
  13. 279
  14. 57
  15. 363
  16. 2
  17. 123
  18. 6
  19. 19
  20. 8
  21. 18
  22. 9
  23. 18
  24. 213
  25. 69
  26. 17
  27. 18
  28. 17
  29. 20
  30. 15
  31. 60
  32. 19
  33. 8
  34. 48
  35. 72
  36. 312
  37. 8
  38. 51
  39. 465
  40. 15

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