← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 1 · 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 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 229 (d) 228
  2. 2.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) 126 (b) 42 (c) 45 (d) 14
  3. 3.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 264 (c) 255 (d) 248
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  5. 5.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 104 (c) 122 (d) 114
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 15 (b) 13 (c) 14 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 8 (b) 5 (c) 7 (d) 6
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 7 (b) 8 (c) 5 (d) 6
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 6 (b) 5 (c) 8 (d) 7
  11. 11.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) 37 (c) 46 (d) 38
  12. 12.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) 27 (b) 9 (c) 81 (d) 30
  13. 13.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) 15 (b) 135 (c) 48 (d) 45
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 3 (d) 13
  15. 15.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
  16. 16.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) 144 (b) 16 (c) 51 (d) 48
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 14 (d) 13
  18. 18.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 261 (c) 271 (d) 252
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  21. 21.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 628 (c) 490 (d) 627
  22. 22.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 247 (c) 236 (d) 246
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  25. 25.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) 72 (b) 24 (c) 75 (d) 216
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 19 (d) 9
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 7 (d) 4
  28. 28.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) 7 (b) 63 (c) 24 (d) 21
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 18 (b) 17 (c) 16 (d) 7
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  32. 32.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) 45 (b) 18 (c) 5 (d) 15
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 17 (d) 16
  34. 34.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 136 (c) 128 (d) 127
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 15 (d) 16
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 4 (c) 3 (d) 2
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  39. 39.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 430 (c) 358 (d) 420
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

  1. 228
  2. 42
  3. 264
  4. 19
  5. 113
  6. 14
  7. 5
  8. 7
  9. 7
  10. 7
  11. 37
  12. 27
  13. 45
  14. 14
  15. 24
  16. 48
  17. 14
  18. 270
  19. 14
  20. 4
  21. 627
  22. 246
  23. 8
  24. 7
  25. 72
  26. 20
  27. 6
  28. 21
  29. 17
  30. 5
  31. 2
  32. 15
  33. 16
  34. 127
  35. 15
  36. 4
  37. 6
  38. 3
  39. 429
  40. 4

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