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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 173 · 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 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 28 (c) 38 (d) 46
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 2 (d) 3
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  5. 5.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 532 (b) 522 (c) 531 (d) 426
  6. 6.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) 24 (c) 75 (d) 72
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 4 (d) 3
  8. 8.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) 51 (d) 144
  9. 9.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 588 (c) 589 (d) 464
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 19 (b) 18 (c) 17 (d) 7
  11. 11.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 450 (c) 460 (d) 378
  12. 12.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 330 (c) 387 (d) 378
  13. 13.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) 21 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  15. 15.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) 10 (b) 33 (c) 90 (d) 30
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 6 (b) 8 (c) 5 (d) 9
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  18. 18.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) 214 (c) 321 (d) 213
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  20. 20.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 189 (c) 180 (d) 198
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 21 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  23. 23.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 225 (c) 226 (d) 222
  24. 24.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) 180 (b) 63 (c) 20 (d) 60
  25. 25.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) 48 (c) 135 (d) 45
  26. 26.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 202 (c) 195 (d) 186
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 9 (c) 7 (d) 8
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 6 (b) 4 (c) 5 (d) 3
  30. 30.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 160 (c) 159 (d) 150
  31. 31.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) 108 (b) 12 (c) 39 (d) 36
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 12 (b) 7 (c) 11 (d) 9
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 19 (b) 18 (c) 7 (d) 17
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 16 (d) 15
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 15 (b) 7 (c) 17 (d) 16
  36. 36.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) 69 (b) 66 (c) 22 (d) 198
  37. 37.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) 54 (c) 18 (d) 21
  38. 38.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 114 (d) 113
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 15 (d) 14
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 18 (d) 19

Answer key

  1. 37
  2. 3
  3. 3
  4. 20
  5. 531
  6. 72
  7. 3
  8. 48
  9. 588
  10. 18
  11. 459
  12. 387
  13. 21
  14. 9
  15. 30
  16. 8
  17. 4
  18. 213
  19. 18
  20. 189
  21. 20
  22. 8
  23. 225
  24. 60
  25. 45
  26. 195
  27. 19
  28. 8
  29. 5
  30. 159
  31. 36
  32. 11
  33. 18
  34. 15
  35. 16
  36. 66
  37. 18
  38. 113
  39. 15
  40. 19

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