← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 861 · 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 5? (a) 4 (b) 6 (c) 10 (d) 5
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 6 (b) 5 (c) 7 (d) 8
  3. 3.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) 45 (c) 14 (d) 42
  4. 4.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) 81 (b) 9 (c) 27 (d) 30
  5. 5.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 39 (c) 12 (d) 108
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 17 (d) 18
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
  8. 8.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) 99 (b) 36 (c) 33 (d) 11
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 21 (d) 9
  10. 10.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 360 (c) 351 (d) 312
  11. 11.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 142 (c) 141 (d) 132
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  13. 13.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 144 (c) 162 (d) 154
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 6 (d) 16
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  16. 16.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 148 (c) 140 (d) 139
  17. 17.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 220 (c) 223 (d) 222
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 3 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  21. 21.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
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  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) 75 (b) 24 (c) 216 (d) 72
  26. 26.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) 27 (d) 24
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  28. 28.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) 51 (c) 48 (d) 144
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 18
  31. 31.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
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 4 (d) 5
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 6 (d) 5
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 4 (c) 12 (d) 14
  35. 35.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 248 (c) 265 (d) 255
  36. 36.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) 5 (b) 15 (c) 18 (d) 45
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 5 (d) 2
  38. 38.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 474 (c) 475 (d) 465
  39. 39.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 39 (d) 13
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 5 (d) 3

Answer key

  1. 5
  2. 7
  3. 42
  4. 27
  5. 36
  6. 18
  7. 16
  8. 33
  9. 20
  10. 360
  11. 141
  12. 7
  13. 153
  14. 17
  15. 2
  16. 139
  17. 222
  18. 5
  19. 6
  20. 3
  21. 564
  22. 2
  23. 17
  24. 8
  25. 72
  26. 24
  27. 3
  28. 48
  29. 5
  30. 19
  31. 17
  32. 5
  33. 5
  34. 13
  35. 264
  36. 15
  37. 4
  38. 474
  39. 39
  40. 4

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