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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 159 · 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 4? (a) 5 (b) 10 (c) 4 (d) 3
  2. 2.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 68 (c) 50 (d) 59
  3. 3.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 74 (d) 84
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 12 (b) 14 (c) 5 (d) 13
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 16 (d) 15
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 1 (b) 4 (c) 2 (d) 3
  7. 7.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) 18 (b) 21 (c) 6 (d) 54
  8. 8.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 103 (c) 104 (d) 94
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 7 (b) 12 (c) 9 (d) 11
  10. 10.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 102 (c) 112 (d) 120
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 16 (c) 15 (d) 5
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  16. 16.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) 69 (c) 207 (d) 72
  17. 17.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) 303 (d) 313
  18. 18.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 205 (c) 204 (d) 208
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 4 (d) 7
  20. 20.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) 198 (b) 66 (c) 22 (d) 69
  21. 21.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) 24 (c) 63 (d) 21
  22. 22.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 144 (c) 51 (d) 48
  23. 23.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) 180 (b) 63 (c) 20 (d) 60
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 19 (d) 18
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  28. 28.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 27 (c) 9 (d) 81
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 4 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  31. 31.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) 11 (c) 36 (d) 99
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  33. 33.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) 153 (b) 54 (c) 17 (d) 51
  34. 34.The numbers 17 to 25 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) 66 (c) 189 (d) 21
  35. 35.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) 30 (b) 33 (c) 10 (d) 90
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 3 (b) 13 (c) 15 (d) 14
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 17 (c) 16 (d) 6
  38. 38.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 148 (c) 139 (d) 140
  39. 39.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 494 (c) 634 (d) 633
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 17 (d) 19

Answer key

  1. 4
  2. 59
  3. 83
  4. 13
  5. 15
  6. 3
  7. 18
  8. 103
  9. 11
  10. 111
  11. 9
  12. 15
  13. 19
  14. 14
  15. 16
  16. 69
  17. 312
  18. 204
  19. 6
  20. 66
  21. 21
  22. 48
  23. 60
  24. 19
  25. 5
  26. 18
  27. 18
  28. 27
  29. 4
  30. 8
  31. 33
  32. 15
  33. 51
  34. 63
  35. 30
  36. 14
  37. 17
  38. 139
  39. 633
  40. 18

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