← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 836 · 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 15? (a) 5 (b) 4 (c) 16 (d) 3
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 6 (d) 18
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 6 (d) 9
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  6. 6.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
  7. 7.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) 57 (c) 60 (d) 171
  8. 8.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 241 (c) 232 (d) 240
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 8 (c) 18 (d) 19
  11. 11.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) 60 (b) 63 (c) 20 (d) 180
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 1
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 5 (b) 4 (c) 2 (d) 3
  15. 15.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) 54 (b) 17 (c) 51 (d) 153
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 21 (b) 9 (c) 19 (d) 20
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  20. 20.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 158 (c) 176 (d) 167
  21. 21.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 38 (c) 46 (d) 37
  22. 22.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) 18 (b) 45 (c) 5 (d) 15
  23. 23.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) 573 (d) 574
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 3 (c) 6 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 21 (d) 9
  26. 26.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 170 (c) 152 (d) 162
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  29. 29.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
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  32. 32.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 577 (c) 576 (d) 456
  33. 33.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 190 (c) 198 (d) 189
  34. 34.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 266 (d) 292
  35. 35.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 64 (c) 72 (d) 63
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 14 (b) 4 (c) 15 (d) 13
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 3 (d) 5
  38. 38.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 357 (d) 348
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
  40. 40.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) 99 (d) 36

Answer key

  1. 4
  2. 17
  3. 8
  4. 15
  5. 5
  6. 27
  7. 57
  8. 240
  9. 6
  10. 18
  11. 60
  12. 19
  13. 3
  14. 4
  15. 51
  16. 3
  17. 20
  18. 9
  19. 9
  20. 167
  21. 37
  22. 15
  23. 573
  24. 5
  25. 20
  26. 161
  27. 4
  28. 3
  29. 54
  30. 7
  31. 8
  32. 576
  33. 189
  34. 291
  35. 63
  36. 14
  37. 4
  38. 357
  39. 16
  40. 33

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