← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 491 · 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 3? (a) 2 (b) 4 (c) 10 (d) 3
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 18 (d) 20
  3. 3.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 252 (d) 261
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 15 (d) 16
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  6. 6.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) 5 (c) 15 (d) 45
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  9. 9.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 532 (c) 531 (d) 522
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 20 (b) 18 (c) 9 (d) 19
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 18 (b) 17 (c) 19 (d) 8
  12. 12.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) 48 (b) 15 (c) 135 (d) 45
  13. 13.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 478 (c) 609 (d) 600
  14. 14.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) 66 (b) 21 (c) 63 (d) 189
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  16. 16.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 32 (c) 50 (d) 42
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 6 (d) 7
  18. 18.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 230 (c) 238 (d) 228
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  20. 20.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 360 (c) 318 (d) 369
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 14 (b) 3 (c) 13 (d) 15
  22. 22.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) 24 (b) 72 (c) 216 (d) 75
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 15 (d) 13
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  26. 26.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) 207 (b) 72 (c) 23 (d) 69
  27. 27.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) 11 (b) 99 (c) 36 (d) 33
  28. 28.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 376 (c) 447 (d) 456
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 9 (d) 21
  30. 30.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) 8 (b) 72 (c) 24 (d) 27
  31. 31.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 459 (c) 384 (d) 469
  32. 32.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
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  34. 34.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 302 (b) 336 (c) 345 (d) 346
  35. 35.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 46 (c) 38 (d) 28
  36. 36.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 124 (c) 106 (d) 116
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 17 (d) 15
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 18
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 6 (b) 7 (c) 4 (d) 5
  40. 40.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) 10 (b) 30 (c) 90 (d) 33

Answer key

  1. 3
  2. 19
  3. 270
  4. 15
  5. 6
  6. 15
  7. 5
  8. 4
  9. 531
  10. 19
  11. 18
  12. 45
  13. 609
  14. 63
  15. 9
  16. 41
  17. 6
  18. 237
  19. 8
  20. 369
  21. 14
  22. 72
  23. 3
  24. 14
  25. 4
  26. 69
  27. 33
  28. 456
  29. 20
  30. 24
  31. 468
  32. 60
  33. 7
  34. 345
  35. 37
  36. 115
  37. 16
  38. 19
  39. 6
  40. 30

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