← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 950 · 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.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) 19 (c) 171 (d) 57
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 3 (c) 4 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  4. 4.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 564 (d) 565
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  7. 7.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 170 (c) 179 (d) 180
  8. 8.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) 63 (c) 189 (d) 21
  9. 9.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 267 (c) 277 (d) 276
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 4 (b) 15 (c) 14 (d) 16
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 6 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  15. 15.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 487 (c) 477 (d) 486
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 20 (c) 19 (d) 9
  17. 17.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 513 (c) 522 (d) 523
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  19. 19.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 630 (c) 640 (d) 639
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 18 (b) 17 (c) 6 (d) 16
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 16 (d) 7
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 21 (d) 20
  26. 26.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 580 (d) 579
  27. 27.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) 16 (b) 48 (c) 144 (d) 51
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
  29. 29.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) 72 (c) 64 (d) 63
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  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) 21 (b) 54 (c) 18 (d) 6
  32. 32.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) 23 (c) 69 (d) 72
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 2 (d) 4
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 4 (c) 3 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  37. 37.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) 51 (b) 17 (c) 54 (d) 153
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 14 (d) 13
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 4 (d) 3

Answer key

  1. 57
  2. 6
  3. 9
  4. 564
  5. 18
  6. 6
  7. 179
  8. 63
  9. 276
  10. 2
  11. 6
  12. 15
  13. 6
  14. 9
  15. 486
  16. 20
  17. 522
  18. 3
  19. 639
  20. 3
  21. 8
  22. 3
  23. 17
  24. 17
  25. 20
  26. 579
  27. 48
  28. 19
  29. 63
  30. 7
  31. 18
  32. 69
  33. 19
  34. 4
  35. 5
  36. 4
  37. 51
  38. 18
  39. 14
  40. 5

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