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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 248 · 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 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 13 (d) 4
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 9 (b) 8 (c) 10 (d) 7
  3. 3.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) 63 (b) 66 (c) 21 (d) 189
  4. 4.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 213 (c) 222 (d) 223
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 5 (d) 3
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 16 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 14 (b) 12 (c) 7 (d) 15
  9. 9.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) 171 (b) 60 (c) 57 (d) 19
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
  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 17? (a) 3 (b) 2 (c) 1 (d) 18
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 8 (d) 19
  18. 18.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 82 (c) 92 (d) 100
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 5 (c) 7 (d) 8
  20. 20.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) 54 (b) 51 (c) 17 (d) 153
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 3 (c) 12 (d) 11
  24. 24.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) 24 (b) 27 (c) 8 (d) 72
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 8 (d) 18
  26. 26.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 549 (c) 558 (d) 559
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
  28. 28.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) 126 (b) 42 (c) 14 (d) 45
  29. 29.The numbers 1 to 9 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) 5 (c) 15 (d) 18
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 5 (c) 4 (d) 6
  31. 31.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 414 (d) 348
  32. 32.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 558 (d) 567
  33. 33.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 370 (c) 438 (d) 448
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  35. 35.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 585 (c) 462 (d) 586
  36. 36.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 517 (c) 416 (d) 507
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  38. 38.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 286 (c) 322 (d) 312
  39. 39.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) 222 (d) 226
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19

Answer key

  1. 14
  2. 9
  3. 63
  4. 222
  5. 4
  6. 17
  7. 9
  8. 14
  9. 57
  10. 20
  11. 18
  12. 17
  13. 21
  14. 2
  15. 3
  16. 16
  17. 19
  18. 91
  19. 7
  20. 51
  21. 18
  22. 5
  23. 11
  24. 24
  25. 19
  26. 558
  27. 16
  28. 42
  29. 15
  30. 6
  31. 414
  32. 567
  33. 447
  34. 6
  35. 585
  36. 516
  37. 7
  38. 321
  39. 225
  40. 19

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