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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 589 · 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.

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  1. 1.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 69 (c) 70 (d) 78
  2. 2.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) 72 (b) 24 (c) 75 (d) 216
  3. 3.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 462 (c) 586 (d) 576
  4. 4.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) 39 (c) 12 (d) 36
  5. 5.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 465 (c) 475 (d) 388
  6. 6.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 343 (c) 300 (d) 342
  7. 7.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) 57 (b) 60 (c) 171 (d) 19
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  10. 10.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 14 (c) 126 (d) 42
  11. 11.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) 21 (b) 63 (c) 189 (d) 66
  12. 12.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 258 (d) 259
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 5 (b) 6 (c) 7 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  16. 16.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 288 (c) 315 (d) 325
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 18
  18. 18.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) 33 (c) 36 (d) 99
  19. 19.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) 51 (b) 17 (c) 153 (d) 54
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3
  21. 21.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) 207 (c) 208 (d) 198
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 8 (d) 18
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 4 (d) 15
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 19 (b) 17 (c) 8 (d) 18
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 17 (d) 5
  27. 27.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 176 (c) 186 (d) 185
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
  29. 29.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) 22 (c) 66 (d) 198
  30. 30.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 489 (c) 404 (d) 499
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 4 (d) 3
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 1 (c) 4 (d) 3
  34. 34.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 84 (d) 75
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 15 (b) 17 (c) 16 (d) 5
  38. 38.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) 7 (b) 63 (c) 24 (d) 21
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 20 (d) 18
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

  1. 69
  2. 72
  3. 585
  4. 36
  5. 474
  6. 342
  7. 57
  8. 7
  9. 3
  10. 42
  11. 63
  12. 258
  13. 7
  14. 6
  15. 4
  16. 324
  17. 19
  18. 33
  19. 51
  20. 3
  21. 207
  22. 19
  23. 15
  24. 8
  25. 18
  26. 16
  27. 185
  28. 15
  29. 66
  30. 498
  31. 4
  32. 4
  33. 3
  34. 75
  35. 5
  36. 5
  37. 16
  38. 21
  39. 19
  40. 3

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