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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 42 · 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 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) 90 (d) 10
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 17 (c) 6 (d) 16
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  5. 5.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 225 (d) 234
  6. 6.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) 18 (b) 54 (c) 21 (d) 6
  7. 7.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 612 (d) 613
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  9. 9.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 138 (d) 137
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 16 (d) 15
  12. 12.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) 33 (b) 11 (c) 36 (d) 99
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 5 (c) 3 (d) 4
  14. 14.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) 108 (c) 99 (d) 100
  15. 15.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) 69 (c) 22 (d) 66
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 19 (d) 7
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 12 (b) 7 (c) 11 (d) 9
  18. 18.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 332 (d) 391
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 6 (b) 4 (c) 5 (d) 7
  23. 23.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) 81 (c) 27 (d) 9
  24. 24.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
  25. 25.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 348 (d) 414
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 20 (d) 19
  29. 29.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 41 (d) 50
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 9 (d) 20
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 6 (b) 8 (c) 9 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 5 (b) 4 (c) 2 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  35. 35.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 182 (c) 173 (d) 174
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 18 (d) 17
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
  38. 38.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 337 (c) 327 (d) 296
  39. 39.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) 45 (b) 18 (c) 15 (d) 5
  40. 40.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 94 (c) 93 (d) 102

Answer key

  1. 30
  2. 17
  3. 9
  4. 8
  5. 234
  6. 18
  7. 612
  8. 9
  9. 137
  10. 7
  11. 16
  12. 33
  13. 4
  14. 99
  15. 66
  16. 18
  17. 11
  18. 390
  19. 5
  20. 2
  21. 6
  22. 6
  23. 27
  24. 39
  25. 414
  26. 8
  27. 5
  28. 19
  29. 41
  30. 20
  31. 8
  32. 3
  33. 4
  34. 2
  35. 173
  36. 18
  37. 18
  38. 336
  39. 15
  40. 93

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