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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 276 · 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 11 to 19 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) 48 (c) 45 (d) 135
  2. 2.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) 173 (c) 174 (d) 182
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 20
  4. 4.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 541 (d) 540
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 5 (b) 4 (c) 2 (d) 3
  8. 8.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) 643 (c) 633 (d) 642
  9. 9.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 82 (c) 73 (d) 64
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 20 (d) 8
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 3 (d) 5
  12. 12.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 565 (d) 564
  13. 13.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) 189 (b) 66 (c) 63 (d) 21
  14. 14.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) 36 (d) 44
  15. 15.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) 36 (b) 39 (c) 108 (d) 12
  16. 16.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) 96 (d) 87
  17. 17.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 85 (c) 94 (d) 86
  18. 18.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) 24 (b) 216 (c) 72 (d) 75
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 12 (c) 4 (d) 14
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  22. 22.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) 81 (d) 27
  23. 23.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) 10 (c) 33 (d) 30
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  27. 27.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 180 (d) 171
  28. 28.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 7 (c) 24 (d) 21
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 2 (c) 4 (d) 3
  30. 30.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) 180 (b) 60 (c) 63 (d) 20
  31. 31.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 324 (c) 294 (d) 334
  32. 32.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 58 (c) 68 (d) 67
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 2 (d) 5
  34. 34.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) 11 (c) 33 (d) 36
  35. 35.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) 72 (b) 27 (c) 24 (d) 8
  36. 36.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 403 (c) 393 (d) 340
  37. 37.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 158 (d) 168
  38. 38.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 95 (c) 96 (d) 86
  39. 39.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 151 (c) 152 (d) 160
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2

Answer key

  1. 45
  2. 173
  3. 19
  4. 540
  5. 9
  6. 5
  7. 4
  8. 642
  9. 73
  10. 19
  11. 4
  12. 564
  13. 63
  14. 35
  15. 36
  16. 87
  17. 85
  18. 72
  19. 8
  20. 13
  21. 9
  22. 27
  23. 30
  24. 7
  25. 3
  26. 2
  27. 171
  28. 21
  29. 4
  30. 60
  31. 333
  32. 67
  33. 4
  34. 33
  35. 24
  36. 402
  37. 167
  38. 95
  39. 151
  40. 2

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