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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 889 · 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 4 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  2. 2.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 160 (c) 169 (d) 170
  3. 3.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 66 (c) 65 (d) 74
  4. 4.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) 153 (d) 17
  5. 5.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 126 (c) 136 (d) 144
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 6 (b) 8 (c) 5 (d) 7
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  10. 10.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) 13 (b) 42 (c) 117 (d) 39
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  12. 12.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) 22 (b) 66 (c) 69 (d) 198
  13. 13.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) 30 (b) 9 (c) 27 (d) 81
  14. 14.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) 5 (b) 45 (c) 18 (d) 15
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 4 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  20. 20.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 12 (d) 108
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 4 (d) 14
  22. 22.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 642 (c) 633 (d) 643
  23. 23.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 64 (c) 55 (d) 56
  24. 24.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 180 (d) 20
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 21 (d) 19
  26. 26.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 258 (d) 270
  27. 27.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) 23 (c) 207 (d) 69
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  29. 29.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 366 (d) 357
  30. 30.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) 33 (c) 10 (d) 90
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 17 (d) 6
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 20 (d) 18
  34. 34.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 543 (c) 534 (d) 434
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  36. 36.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 264 (c) 289 (d) 288
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  38. 38.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) 75 (b) 24 (c) 72 (d) 216
  39. 39.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) 8 (b) 27 (c) 72 (d) 24
  40. 40.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 612 (c) 613 (d) 480

Answer key

  1. 3
  2. 169
  3. 65
  4. 51
  5. 135
  6. 7
  7. 5
  8. 4
  9. 3
  10. 39
  11. 4
  12. 66
  13. 27
  14. 15
  15. 9
  16. 4
  17. 8
  18. 20
  19. 19
  20. 36
  21. 15
  22. 642
  23. 55
  24. 60
  25. 20
  26. 279
  27. 69
  28. 4
  29. 366
  30. 30
  31. 5
  32. 17
  33. 19
  34. 543
  35. 2
  36. 288
  37. 8
  38. 72
  39. 24
  40. 612

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