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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 629 · 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 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 52 (c) 61 (d) 70
  2. 2.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 56 (c) 46 (d) 64
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 5 (d) 6
  4. 4.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 180 (d) 171
  5. 5.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) 144 (c) 162 (d) 154
  6. 6.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 150 (c) 159 (d) 168
  7. 7.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) 81 (b) 30 (c) 27 (d) 9
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 17 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  10. 10.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) 33 (b) 90 (c) 30 (d) 10
  11. 11.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 390 (c) 477 (d) 468
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  13. 13.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
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 20 (d) 19
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  16. 16.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) 18 (b) 15 (c) 5 (d) 45
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  20. 20.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  22. 22.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 118 (c) 127 (d) 128
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 15 (b) 4 (c) 14 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 8 (b) 6 (c) 5 (d) 7
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 17 (d) 16
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 17 (d) 8
  30. 30.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 110 (c) 118 (d) 109
  31. 31.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 103 (c) 104 (d) 94
  32. 32.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 364 (c) 363 (d) 354
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 7 (b) 8 (c) 10 (d) 9
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  35. 35.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 318 (c) 360 (d) 369
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 21 (d) 20
  37. 37.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) 48 (b) 45 (c) 15 (d) 135
  38. 38.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 4 (d) 3
  40. 40.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 35 (c) 36 (d) 26

Answer key

  1. 61
  2. 55
  3. 5
  4. 171
  5. 153
  6. 159
  7. 27
  8. 17
  9. 8
  10. 30
  11. 477
  12. 2
  13. 66
  14. 20
  15. 7
  16. 15
  17. 3
  18. 20
  19. 6
  20. 177
  21. 4
  22. 127
  23. 20
  24. 3
  25. 15
  26. 4
  27. 7
  28. 16
  29. 18
  30. 109
  31. 103
  32. 363
  33. 9
  34. 3
  35. 369
  36. 20
  37. 45
  38. 9
  39. 4
  40. 35

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