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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 140 · 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 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) 81 (b) 27 (c) 9 (d) 30
  2. 2.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) 12 (c) 108 (d) 36
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  5. 5.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 176 (c) 194 (d) 186
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 18
  7. 7.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 62 (c) 71 (d) 72
  8. 8.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) 66 (c) 189 (d) 63
  9. 9.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 576 (c) 456 (d) 577
  10. 10.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) 45 (b) 126 (c) 42 (d) 14
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  12. 12.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 501 (c) 492 (d) 502
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  14. 14.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 147 (c) 148 (d) 156
  15. 15.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) 20 (b) 180 (c) 60 (d) 63
  16. 16.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) 54 (c) 6 (d) 18
  17. 17.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 100 (d) 109
  18. 18.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 57 (d) 66
  19. 19.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 432 (c) 433 (d) 423
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 9 (b) 15 (c) 18 (d) 17
  21. 21.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) 11 (b) 36 (c) 33 (d) 99
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 18 (d) 17
  23. 23.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
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  25. 25.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) 48 (c) 16 (d) 144
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 3 (d) 4
  29. 29.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) 51 (d) 54
  30. 30.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) 18 (b) 57 (c) 54 (d) 162
  31. 31.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 100 (c) 99 (d) 108
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 12 (b) 4 (c) 11 (d) 10
  33. 33.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 472 (d) 601
  34. 34.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 144 (c) 136 (d) 135
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  36. 36.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 88 (c) 87 (d) 96
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 17 (d) 18
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 7 (d) 5
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2

Answer key

  1. 27
  2. 36
  3. 3
  4. 7
  5. 185
  6. 19
  7. 71
  8. 63
  9. 576
  10. 42
  11. 4
  12. 501
  13. 7
  14. 147
  15. 60
  16. 18
  17. 109
  18. 57
  19. 432
  20. 17
  21. 33
  22. 17
  23. 15
  24. 2
  25. 48
  26. 9
  27. 5
  28. 5
  29. 51
  30. 54
  31. 99
  32. 11
  33. 600
  34. 135
  35. 16
  36. 87
  37. 17
  38. 6
  39. 6
  40. 3

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