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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 286 · 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 two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 17 (d) 16
  3. 3.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) 66 (b) 69 (c) 22 (d) 198
  4. 4.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) 171 (b) 19 (c) 57 (d) 60
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 3 (d) 2
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  8. 8.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) 48 (b) 45 (c) 15 (d) 135
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  11. 11.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) 33 (c) 36 (d) 99
  12. 12.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) 69 (b) 207 (c) 72 (d) 23
  13. 13.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 41 (c) 32 (d) 42
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  15. 15.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 589 (c) 588 (d) 464
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 20 (d) 19
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 5 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  22. 22.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 71 (c) 80 (d) 62
  23. 23.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) 162 (b) 18 (c) 54 (d) 57
  24. 24.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 558 (c) 559 (d) 549
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 5 (c) 4 (d) 3
  27. 27.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 162 (c) 161 (d) 152
  28. 28.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 519 (c) 520 (d) 418
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  32. 32.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) 51 (b) 153 (c) 54 (d) 17
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  34. 34.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 458 (d) 579
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  37. 37.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 149 (d) 140
  38. 38.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 331 (c) 292 (d) 321
  39. 39.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) 14 (d) 42
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 6 (d) 3

Answer key

  1. 4
  2. 16
  3. 66
  4. 57
  5. 6
  6. 4
  7. 6
  8. 45
  9. 8
  10. 3
  11. 33
  12. 69
  13. 41
  14. 2
  15. 588
  16. 19
  17. 17
  18. 5
  19. 9
  20. 3
  21. 18
  22. 71
  23. 54
  24. 558
  25. 20
  26. 4
  27. 161
  28. 519
  29. 5
  30. 3
  31. 9
  32. 51
  33. 7
  34. 579
  35. 18
  36. 20
  37. 149
  38. 330
  39. 42
  40. 5

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