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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 791 · 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 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 170 (c) 162 (d) 161
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  3. 3.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 90 (c) 100 (d) 108
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  5. 5.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 342 (c) 351 (d) 306
  6. 6.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 453 (c) 380 (d) 462
  7. 7.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 81 (c) 27 (d) 30
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 1 (d) 3
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 3 (b) 5 (c) 2 (d) 4
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 15 (b) 14 (c) 5 (d) 16
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 20 (d) 18
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 14 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  15. 15.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 72 (c) 64 (d) 63
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 19 (d) 9
  17. 17.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) 189 (c) 66 (d) 63
  18. 18.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 585 (c) 594 (d) 468
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  20. 20.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) 162 (c) 18 (d) 54
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 15 (d) 16
  22. 22.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 57 (d) 58
  23. 23.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) 24 (b) 216 (c) 75 (d) 72
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 17 (d) 19
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 15 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  27. 27.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 292 (d) 266
  28. 28.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 456 (d) 457
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  30. 30.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 421 (c) 411 (d) 352
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 18 (d) 16
  32. 32.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 40 (c) 31 (d) 22
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 14 (b) 13 (c) 15 (d) 3
  34. 34.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) 72 (b) 69 (c) 207 (d) 23
  35. 35.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 280 (d) 303
  36. 36.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 436 (c) 547 (d) 537
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 18 (d) 17
  38. 38.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  39. 39.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) 6 (c) 21 (d) 18
  40. 40.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) 198 (b) 66 (c) 22 (d) 69

Answer key

  1. 161
  2. 4
  3. 99
  4. 5
  5. 351
  6. 462
  7. 27
  8. 3
  9. 4
  10. 15
  11. 5
  12. 19
  13. 15
  14. 3
  15. 63
  16. 20
  17. 63
  18. 594
  19. 8
  20. 54
  21. 16
  22. 57
  23. 72
  24. 18
  25. 15
  26. 6
  27. 291
  28. 456
  29. 9
  30. 420
  31. 17
  32. 31
  33. 14
  34. 69
  35. 312
  36. 546
  37. 17
  38. 7
  39. 18
  40. 66

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