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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 59 · 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 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  2. 2.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 74 (c) 56 (d) 66
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 4 (c) 5 (d) 6
  4. 4.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 40 (c) 58 (d) 50
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 16 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  7. 7.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) 69 (b) 72 (c) 23 (d) 207
  8. 8.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 78 (c) 68 (d) 77
  9. 9.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 31 (c) 22 (d) 32
  10. 10.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 552 (c) 553 (d) 543
  11. 11.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 271 (c) 270 (d) 252
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  13. 13.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) 72 (b) 216 (c) 75 (d) 24
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 6 (c) 16 (d) 17
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  20. 20.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
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 7 (c) 18 (d) 17
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 15 (b) 16 (c) 5 (d) 17
  25. 25.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) 21 (b) 18 (c) 6 (d) 54
  26. 26.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) 17 (c) 54 (d) 51
  27. 27.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) 27 (b) 81 (c) 30 (d) 9
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 21 (d) 9
  29. 29.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 26 (c) 44 (d) 36
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 6 (b) 7 (c) 8 (d) 5
  31. 31.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) 15 (b) 5 (c) 45 (d) 18
  32. 32.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 140 (c) 150 (d) 158
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 16 (c) 6 (d) 17
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  35. 35.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 391 (d) 381
  36. 36.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 462 (c) 576 (d) 586
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 20 (d) 21
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 9 (b) 10 (c) 7 (d) 8
  39. 39.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 216 (c) 324 (d) 217
  40. 40.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 438 (c) 370 (d) 447

Answer key

  1. 18
  2. 65
  3. 5
  4. 49
  5. 17
  6. 5
  7. 69
  8. 77
  9. 31
  10. 552
  11. 270
  12. 9
  13. 72
  14. 8
  15. 17
  16. 4
  17. 17
  18. 3
  19. 4
  20. 91
  21. 2
  22. 3
  23. 18
  24. 16
  25. 18
  26. 51
  27. 27
  28. 20
  29. 35
  30. 7
  31. 15
  32. 149
  33. 16
  34. 6
  35. 390
  36. 585
  37. 20
  38. 9
  39. 216
  40. 447

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