← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 960 · 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 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) 48 (b) 51 (c) 16 (d) 144
  2. 2.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 315 (c) 324 (d) 325
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  6. 6.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 537 (d) 538
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 7 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  9. 9.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
  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) 81 (b) 30 (c) 9 (d) 27
  11. 11.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
  12. 12.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 130 (d) 140
  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) 135 (b) 48 (c) 15 (d) 45
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 15
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  17. 17.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) 27 (b) 8 (c) 72 (d) 24
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 8 (d) 19
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 3 (d) 1
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  22. 22.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 607 (c) 597 (d) 476
  23. 23.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 262 (d) 246
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 17 (d) 16
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  26. 26.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  27. 27.The numbers 18 to 26 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) 198 (c) 69 (d) 22
  28. 28.The numbers 14 to 22 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) 57 (c) 162 (d) 18
  29. 29.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 405 (c) 414 (d) 415
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 16 (d) 17
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  32. 32.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 102 (c) 101 (d) 110
  33. 33.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 94 (c) 103 (d) 112
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 5 (d) 3
  35. 35.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) 108 (c) 39 (d) 12
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 4 (d) 3
  38. 38.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 112 (c) 121 (d) 122
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 19 (d) 17
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19

Answer key

  1. 48
  2. 324
  3. 19
  4. 3
  5. 7
  6. 537
  7. 7
  8. 8
  9. 30
  10. 27
  11. 69
  12. 139
  13. 45
  14. 16
  15. 5
  16. 4
  17. 24
  18. 2
  19. 19
  20. 3
  21. 9
  22. 606
  23. 261
  24. 16
  25. 3
  26. 177
  27. 66
  28. 54
  29. 414
  30. 16
  31. 6
  32. 101
  33. 103
  34. 4
  35. 36
  36. 8
  37. 4
  38. 121
  39. 18
  40. 19

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