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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 754 · 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 5 written when you write all the numbers from 1 to 62? (a) 16 (b) 6 (c) 17 (d) 15
  2. 2.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) 24 (c) 7 (d) 21
  3. 3.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) 180 (c) 63 (d) 20
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  7. 7.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) 10 (b) 33 (c) 90 (d) 30
  8. 8.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 159 (d) 160
  9. 9.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) 99 (c) 11 (d) 36
  10. 10.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) 162 (c) 57 (d) 54
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  12. 12.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 90 (d) 81
  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) 75 (b) 216 (c) 24 (d) 72
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  16. 16.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) 68 (c) 67 (d) 58
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 17 (d) 18
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 15 (d) 3
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 20 (d) 19
  20. 20.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 171 (c) 60 (d) 19
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 20 (d) 9
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 17 (b) 14 (c) 9 (d) 16
  23. 23.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 400 (c) 493 (d) 492
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  25. 25.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) 23 (b) 72 (c) 69 (d) 207
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  27. 27.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 280 (c) 313 (d) 303
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 15 (d) 17
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  30. 30.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) 14 (b) 45 (c) 42 (d) 126
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 16 (d) 6
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 15 (b) 4 (c) 16 (d) 14
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  34. 34.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 288 (d) 279
  35. 35.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 459 (c) 450 (d) 460
  36. 36.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) 12 (c) 39 (d) 108
  37. 37.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 148 (c) 130 (d) 140
  38. 38.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 555 (c) 448 (d) 564
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
  40. 40.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 330 (c) 339 (d) 298

Answer key

  1. 16
  2. 21
  3. 60
  4. 6
  5. 19
  6. 20
  7. 30
  8. 159
  9. 33
  10. 54
  11. 4
  12. 81
  13. 72
  14. 9
  15. 2
  16. 67
  17. 18
  18. 14
  19. 19
  20. 57
  21. 20
  22. 16
  23. 492
  24. 4
  25. 69
  26. 20
  27. 312
  28. 16
  29. 3
  30. 42
  31. 17
  32. 15
  33. 18
  34. 288
  35. 459
  36. 36
  37. 139
  38. 564
  39. 5
  40. 339

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