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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 282 · 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.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 5 (d) 17
  2. 2.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 367 (c) 366 (d) 357
  3. 3.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) 90 (c) 30 (d) 33
  4. 4.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) 8 (c) 72 (d) 24
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  6. 6.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) 63 (b) 20 (c) 60 (d) 180
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 4 (d) 2
  8. 8.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 270 (c) 279 (d) 258
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 7 (b) 8 (c) 5 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  12. 12.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) 126 (c) 14 (d) 42
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
  14. 14.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) 75 (b) 24 (c) 216 (d) 72
  15. 15.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) 16 (b) 144 (c) 51 (d) 48
  16. 16.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 82 (d) 91
  17. 17.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) 45 (c) 135 (d) 48
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 15 (d) 16
  19. 19.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 618 (c) 484 (d) 609
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 5 (d) 17
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 13 (d) 14
  27. 27.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 130 (c) 138 (d) 120
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  29. 29.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 253 (d) 252
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 19 (c) 20 (d) 9
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 5 (b) 16 (c) 15 (d) 17
  32. 32.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 207 (c) 72 (d) 69
  33. 33.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) 17 (b) 153 (c) 51 (d) 54
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 18 (d) 7
  35. 35.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 478 (d) 609
  36. 36.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 639 (c) 640 (d) 498
  37. 37.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 406 (c) 492 (d) 501
  38. 38.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 242 (c) 246 (d) 256
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5
  40. 40.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 178 (c) 188 (d) 196

Answer key

  1. 16
  2. 366
  3. 30
  4. 24
  5. 6
  6. 60
  7. 4
  8. 279
  9. 8
  10. 7
  11. 2
  12. 42
  13. 20
  14. 72
  15. 48
  16. 91
  17. 45
  18. 16
  19. 618
  20. 7
  21. 17
  22. 4
  23. 16
  24. 3
  25. 9
  26. 13
  27. 129
  28. 8
  29. 252
  30. 20
  31. 16
  32. 69
  33. 51
  34. 17
  35. 609
  36. 639
  37. 501
  38. 255
  39. 4
  40. 187

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