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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 711 · 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 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
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 12 (b) 9 (c) 15 (d) 14
  4. 4.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
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 5 (d) 3
  6. 6.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
  7. 7.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 76 (c) 75 (d) 84
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  9. 9.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) 36 (d) 108
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  12. 12.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 146 (d) 155
  13. 13.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 492 (c) 493 (d) 483
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  15. 15.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 50 (c) 32 (d) 41
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 4 (d) 2
  17. 17.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  18. 18.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 166 (d) 165
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 6 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  21. 21.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 154 (d) 144
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  23. 23.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) 36 (b) 33 (c) 11 (d) 99
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 1 (d) 4
  25. 25.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 57 (d) 66
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  28. 28.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 603 (d) 613
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  30. 30.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) 86 (d) 104
  31. 31.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) 207 (d) 208
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  33. 33.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) 27 (b) 24 (c) 8 (d) 72
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 17 (b) 5 (c) 15 (d) 16
  36. 36.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 564 (c) 454 (d) 574
  37. 37.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) 63 (c) 180 (d) 60
  38. 38.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) 198 (d) 69
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 16 (b) 7 (c) 18 (d) 17
  40. 40.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 380 (c) 463 (d) 462

Answer key

  1. 57
  2. 4
  3. 14
  4. 267
  5. 5
  6. 15
  7. 75
  8. 9
  9. 36
  10. 4
  11. 7
  12. 155
  13. 492
  14. 9
  15. 41
  16. 3
  17. 8
  18. 165
  19. 6
  20. 4
  21. 153
  22. 6
  23. 33
  24. 3
  25. 57
  26. 2
  27. 7
  28. 612
  29. 5
  30. 95
  31. 207
  32. 8
  33. 24
  34. 3
  35. 16
  36. 573
  37. 60
  38. 66
  39. 17
  40. 462

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