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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 10 · 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 6? (a) 10 (b) 7 (c) 5 (d) 6
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  3. 3.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) 54 (c) 153 (d) 17
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 5 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  7. 7.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 435 (c) 445 (d) 368
  8. 8.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) 15 (c) 5 (d) 45
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 16 (d) 7
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 6 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  13. 13.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 144 (c) 143 (d) 152
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 10 (b) 5 (c) 9 (d) 7
  15. 15.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) 54 (b) 6 (c) 21 (d) 18
  16. 16.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 60 (c) 68 (d) 59
  17. 17.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) 135 (d) 15
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 4 (d) 5
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 8 (b) 10 (c) 6 (d) 11
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 13 (d) 14
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 18 (b) 20 (c) 9 (d) 19
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 15 (d) 14
  24. 24.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 417 (d) 350
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 16 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  27. 27.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 44 (c) 43 (d) 52
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 5 (c) 4 (d) 6
  29. 29.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 150 (c) 142 (d) 141
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 5 (b) 6 (c) 4 (d) 3
  31. 31.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) 7 (b) 63 (c) 24 (d) 21
  32. 32.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 16 (b) 9 (c) 19 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  37. 37.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 330 (c) 388 (d) 387
  38. 38.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 46 (c) 28 (d) 38
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10

Answer key

  1. 6
  2. 20
  3. 51
  4. 6
  5. 4
  6. 2
  7. 444
  8. 15
  9. 17
  10. 6
  11. 8
  12. 9
  13. 143
  14. 9
  15. 18
  16. 59
  17. 45
  18. 5
  19. 17
  20. 10
  21. 14
  22. 19
  23. 15
  24. 417
  25. 17
  26. 3
  27. 43
  28. 6
  29. 141
  30. 5
  31. 21
  32. 300
  33. 3
  34. 18
  35. 7
  36. 6
  37. 387
  38. 37
  39. 18
  40. 5

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