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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 838 · 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 52? (a) 9 (b) 6 (c) 8 (d) 5
  2. 2.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) 45 (b) 15 (c) 48 (d) 135
  3. 3.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) 24 (c) 27 (d) 8
  4. 4.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 486 (c) 612 (d) 621
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
  6. 6.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) 24 (b) 63 (c) 21 (d) 7
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
  8. 8.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) 33 (c) 30 (d) 10
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 3 (b) 4 (c) 5 (d) 6
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 18 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
  13. 13.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 124 (c) 116 (d) 115
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  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) 108 (b) 39 (c) 12 (d) 36
  16. 16.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 85 (d) 76
  17. 17.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) 21 (c) 6 (d) 18
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 20 (b) 18 (c) 8 (d) 19
  25. 25.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) 63 (b) 180 (c) 60 (d) 20
  26. 26.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) 39 (b) 117 (c) 42 (d) 13
  27. 27.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 591 (c) 601 (d) 600
  28. 28.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) 69 (b) 22 (c) 198 (d) 66
  29. 29.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 154 (c) 162 (d) 144
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 4 (d) 15
  32. 32.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) 57 (c) 54 (d) 18
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 3 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 17
  36. 36.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 358 (c) 420 (d) 430
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 16 (d) 5
  39. 39.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) 17 (b) 54 (c) 153 (d) 51
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 4 (c) 10 (d) 11

Answer key

  1. 8
  2. 45
  3. 24
  4. 621
  5. 18
  6. 21
  7. 5
  8. 30
  9. 5
  10. 18
  11. 7
  12. 18
  13. 115
  14. 8
  15. 36
  16. 85
  17. 18
  18. 2
  19. 9
  20. 7
  21. 3
  22. 5
  23. 3
  24. 19
  25. 60
  26. 39
  27. 600
  28. 66
  29. 153
  30. 20
  31. 15
  32. 54
  33. 4
  34. 5
  35. 18
  36. 429
  37. 4
  38. 16
  39. 51
  40. 10

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