← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 16 · 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 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 303 (d) 274
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 19 (d) 18
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 3 (d) 6
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 15 (b) 14 (c) 5 (d) 16
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 5 (d) 4
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 18 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  10. 10.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) 81 (c) 9 (d) 27
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  13. 13.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 56 (c) 46 (d) 55
  14. 14.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 451 (c) 450 (d) 441
  15. 15.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 72 (d) 24
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 4 (d) 15
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 2 (b) 5 (c) 3 (d) 4
  18. 18.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) 15 (c) 5 (d) 45
  19. 19.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) 19 (d) 57
  20. 20.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) 104 (c) 103 (d) 94
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  22. 22.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 190 (d) 180
  23. 23.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 68 (d) 58
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 16 (d) 14
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  26. 26.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) 63 (b) 21 (c) 24 (d) 7
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 7 (c) 5 (d) 6
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  29. 29.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 486 (c) 477 (d) 396
  30. 30.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) 45 (c) 15 (d) 48
  31. 31.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) 6 (c) 21 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  33. 33.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 421 (c) 420 (d) 411
  34. 34.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 234 (c) 228 (d) 235
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 21 (d) 9
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 16 (d) 15
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  38. 38.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) 72 (c) 69 (d) 207
  39. 39.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 370 (c) 448 (d) 447
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18

Answer key

  1. 303
  2. 19
  3. 5
  4. 3
  5. 15
  6. 4
  7. 19
  8. 5
  9. 2
  10. 27
  11. 7
  12. 2
  13. 55
  14. 450
  15. 72
  16. 15
  17. 4
  18. 15
  19. 57
  20. 103
  21. 7
  22. 189
  23. 67
  24. 15
  25. 4
  26. 21
  27. 7
  28. 4
  29. 486
  30. 45
  31. 18
  32. 9
  33. 420
  34. 234
  35. 20
  36. 15
  37. 20
  38. 69
  39. 447
  40. 18

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