← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 940 · 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 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 162 (c) 171 (d) 172
  2. 2.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 615 (d) 482
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  4. 4.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 535 (c) 534 (d) 428
  5. 5.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) 9 (b) 81 (c) 30 (d) 27
  6. 6.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) 22 (c) 69 (d) 66
  7. 7.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) 135 (b) 48 (c) 45 (d) 15
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 5 (d) 4
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  10. 10.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) 15 (b) 45 (c) 5 (d) 18
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 7 (b) 4 (c) 5 (d) 6
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 5 (d) 3
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 3 (d) 4
  15. 15.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
  16. 16.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) 60 (b) 171 (c) 57 (d) 19
  17. 17.The numbers 10 to 18 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) 14 (c) 45 (d) 126
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 5 (b) 4 (c) 6 (d) 3
  19. 19.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) 13 (b) 39 (c) 117 (d) 42
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  22. 22.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) 189 (b) 63 (c) 66 (d) 21
  23. 23.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 154 (c) 164 (d) 172
  24. 24.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 158 (c) 157 (d) 166
  25. 25.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) 94 (c) 103 (d) 104
  26. 26.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) 8 (c) 24 (d) 72
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  32. 32.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 187 (c) 188 (d) 178
  33. 33.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) 36 (b) 108 (c) 39 (d) 12
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 9 (b) 8 (c) 7 (d) 6
  36. 36.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 21 (d) 9

Answer key

  1. 171
  2. 615
  3. 3
  4. 534
  5. 27
  6. 66
  7. 45
  8. 6
  9. 17
  10. 15
  11. 6
  12. 5
  13. 17
  14. 5
  15. 60
  16. 57
  17. 42
  18. 5
  19. 39
  20. 18
  21. 4
  22. 63
  23. 163
  24. 157
  25. 103
  26. 24
  27. 19
  28. 7
  29. 5
  30. 4
  31. 2
  32. 187
  33. 36
  34. 6
  35. 8
  36. 258
  37. 2
  38. 4
  39. 19
  40. 20

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad