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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 825 · 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 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 98 (c) 89 (d) 90
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 6 (b) 5 (c) 3 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 1 (d) 4
  6. 6.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 136 (c) 146 (d) 154
  7. 7.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 391 (c) 381 (d) 332
  8. 8.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 216 (c) 226 (d) 225
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 1
  13. 13.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 140 (d) 149
  14. 14.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) 21 (c) 63 (d) 24
  15. 15.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 417 (c) 418 (d) 408
  16. 16.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 59 (c) 68 (d) 50
  17. 17.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) 75 (c) 216 (d) 24
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  19. 19.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) 69 (c) 198 (d) 66
  20. 20.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 564 (c) 573 (d) 454
  21. 21.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) 162 (b) 18 (c) 57 (d) 54
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 5 (b) 7 (c) 4 (d) 6
  24. 24.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 144 (c) 143 (d) 152
  25. 25.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 433 (c) 360 (d) 432
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  30. 30.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 88 (c) 106 (d) 97
  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) 39 (b) 12 (c) 108 (d) 36
  32. 32.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 117 (c) 39 (d) 13
  33. 33.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) 21 (c) 54 (d) 18
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 1 (b) 3 (c) 2 (d) 4
  36. 36.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) 72 (b) 24 (c) 27 (d) 8
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 5 (d) 2
  38. 38.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
  39. 39.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 68 (c) 67 (d) 58
  40. 40.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 240 (c) 238 (d) 250

Answer key

  1. 89
  2. 5
  3. 6
  4. 2
  5. 3
  6. 145
  7. 390
  8. 225
  9. 19
  10. 2
  11. 3
  12. 3
  13. 149
  14. 21
  15. 417
  16. 59
  17. 72
  18. 4
  19. 66
  20. 573
  21. 54
  22. 9
  23. 6
  24. 143
  25. 432
  26. 5
  27. 8
  28. 3
  29. 4
  30. 97
  31. 36
  32. 39
  33. 18
  34. 17
  35. 3
  36. 24
  37. 4
  38. 60
  39. 67
  40. 249

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