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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 284 · 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.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 94 (d) 102
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  3. 3.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) 39 (b) 36 (c) 108 (d) 12
  4. 4.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 108 (c) 116 (d) 107
  5. 5.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 250 (c) 258 (d) 267
  6. 6.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 159 (c) 160 (d) 168
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 7 (b) 6 (c) 9 (d) 8
  8. 8.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) 27 (b) 72 (c) 24 (d) 8
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 18
  13. 13.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) 6 (b) 18 (c) 54 (d) 21
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  15. 15.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 331 (c) 330 (d) 321
  16. 16.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) 10 (c) 33 (d) 90
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 20 (d) 9
  19. 19.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 155 (c) 156 (d) 164
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 18 (d) 7
  22. 22.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) 48 (c) 15 (d) 135
  23. 23.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) 19 (b) 60 (c) 171 (d) 57
  24. 24.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 213 (d) 222
  25. 25.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 42 (c) 60 (d) 51
  26. 26.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 17
  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) 66 (b) 198 (c) 22 (d) 69
  29. 29.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) 21 (b) 63 (c) 24 (d) 7
  30. 30.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) 144 (b) 48 (c) 51 (d) 16
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  32. 32.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
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 20 (d) 19
  34. 34.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) 20 (c) 60 (d) 63
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 18 (d) 20
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  37. 37.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 564 (c) 574 (d) 573
  38. 38.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 112 (c) 103 (d) 104
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 2 (d) 4
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3

Answer key

  1. 93
  2. 9
  3. 36
  4. 107
  5. 267
  6. 159
  7. 8
  8. 24
  9. 7
  10. 2
  11. 3
  12. 19
  13. 18
  14. 15
  15. 330
  16. 30
  17. 9
  18. 19
  19. 155
  20. 8
  21. 18
  22. 45
  23. 57
  24. 222
  25. 51
  26. 6
  27. 18
  28. 66
  29. 21
  30. 48
  31. 18
  32. 33
  33. 19
  34. 60
  35. 19
  36. 5
  37. 573
  38. 103
  39. 4
  40. 4

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