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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 452 · 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.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) 153 (b) 51 (c) 17 (d) 54
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  3. 3.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
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 7 (b) 9 (c) 12 (d) 11
  6. 6.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) 18 (b) 45 (c) 15 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 2 (d) 4
  11. 11.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 318 (c) 328 (d) 327
  12. 12.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  13. 13.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 18 (d) 6
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 5 (d) 16
  18. 18.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 210 (c) 208 (d) 207
  19. 19.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 53 (d) 62
  20. 20.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 149 (d) 140
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 9 (d) 20
  22. 22.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) 90 (b) 33 (c) 30 (d) 10
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 9 (c) 5 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  25. 25.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 11 (d) 36
  26. 26.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 505 (c) 495 (d) 504
  27. 27.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 410 (c) 507 (d) 498
  28. 28.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) 48 (d) 144
  29. 29.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 513 (c) 504 (d) 514
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  32. 32.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 342 (c) 406 (d) 405
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 16 (d) 15
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 4 (d) 14
  37. 37.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) 117 (b) 13 (c) 39 (d) 42
  38. 38.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 71 (d) 62
  39. 39.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 412 (d) 511
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 5 (c) 4 (d) 7

Answer key

  1. 51
  2. 8
  3. 42
  4. 3
  5. 11
  6. 15
  7. 5
  8. 16
  9. 20
  10. 3
  11. 327
  12. 9
  13. 4
  14. 4
  15. 17
  16. 6
  17. 16
  18. 207
  19. 53
  20. 149
  21. 19
  22. 30
  23. 8
  24. 8
  25. 33
  26. 504
  27. 507
  28. 48
  29. 513
  30. 5
  31. 2
  32. 405
  33. 16
  34. 3
  35. 19
  36. 15
  37. 39
  38. 71
  39. 510
  40. 6

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