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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 856 · 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 7 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  4. 4.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) 42 (b) 13 (c) 39 (d) 117
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 10 (c) 12 (d) 13
  6. 6.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) 5 (c) 18 (d) 15
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  8. 8.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 66 (d) 57
  9. 9.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 356 (c) 427 (d) 417
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 7 (d) 16
  11. 11.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 111 (c) 120 (d) 112
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 16 (d) 4
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 14 (b) 3 (c) 13 (d) 12
  14. 14.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) 22 (c) 198 (d) 69
  15. 15.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) 33 (b) 10 (c) 90 (d) 30
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 16 (b) 15 (c) 6 (d) 17
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 17 (d) 18
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 17 (d) 8
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 5 (b) 4 (c) 3 (d) 6
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 6 (c) 5 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  26. 26.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) 12 (b) 39 (c) 36 (d) 108
  27. 27.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 87 (c) 88 (d) 78
  28. 28.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 336 (c) 396 (d) 397
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  31. 31.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 375 (c) 366 (d) 322
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 11 (d) 10
  33. 33.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) 57 (b) 18 (c) 162 (d) 54
  34. 34.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) 21 (b) 54 (c) 6 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 4 (d) 5
  37. 37.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 69 (c) 60 (d) 78
  38. 38.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 94 (d) 86
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 4 (d) 15
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4

Answer key

  1. 4
  2. 8
  3. 4
  4. 39
  5. 12
  6. 15
  7. 4
  8. 57
  9. 426
  10. 17
  11. 111
  12. 15
  13. 13
  14. 66
  15. 30
  16. 16
  17. 18
  18. 18
  19. 20
  20. 5
  21. 6
  22. 6
  23. 5
  24. 6
  25. 3
  26. 36
  27. 87
  28. 396
  29. 19
  30. 7
  31. 375
  32. 11
  33. 54
  34. 18
  35. 3
  36. 5
  37. 69
  38. 85
  39. 15
  40. 5

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