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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 214 · 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 8 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 6 (d) 4
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
  3. 3.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) 54 (c) 153 (d) 51
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 17 (d) 18
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 3 (d) 15
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 17 (d) 6
  7. 7.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) 51 (b) 16 (c) 144 (d) 48
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 14 (d) 15
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 4 (b) 8 (c) 6 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  11. 11.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 494 (c) 634 (d) 624
  12. 12.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) 30 (b) 10 (c) 90 (d) 33
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 5 (b) 3 (c) 4 (d) 6
  15. 15.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) 432 (d) 360
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  17. 17.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 326 (d) 381
  18. 18.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) 186 (c) 195 (d) 202
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 9 (c) 7 (d) 6
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  21. 21.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) 48 (d) 135
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 16 (b) 6 (c) 17 (d) 15
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 17 (d) 18
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 16 (d) 7
  25. 25.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 94 (d) 85
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  28. 28.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 354 (c) 424 (d) 414
  29. 29.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 628 (c) 618 (d) 490
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  32. 32.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 90 (c) 80 (d) 89
  33. 33.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 34 (c) 24 (d) 42
  34. 34.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 348 (c) 304 (d) 339
  35. 35.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 37 (c) 38 (d) 46
  36. 36.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) 75 (c) 72 (d) 24
  37. 37.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
  38. 38.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) 57 (b) 54 (c) 162 (d) 18
  39. 39.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 496 (d) 636
  40. 40.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) 54 (b) 21 (c) 18 (d) 6

Answer key

  1. 5
  2. 4
  3. 51
  4. 18
  5. 14
  6. 17
  7. 48
  8. 15
  9. 8
  10. 3
  11. 633
  12. 30
  13. 5
  14. 5
  15. 432
  16. 9
  17. 381
  18. 195
  19. 8
  20. 17
  21. 45
  22. 16
  23. 17
  24. 17
  25. 85
  26. 7
  27. 8
  28. 423
  29. 627
  30. 8
  31. 6
  32. 89
  33. 33
  34. 348
  35. 37
  36. 72
  37. 57
  38. 54
  39. 636
  40. 18

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