← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 178 · 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 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 258 (d) 259
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  4. 4.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) 18 (b) 6 (c) 21 (d) 54
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 8 (b) 6 (c) 7 (d) 5
  6. 6.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) 45 (c) 15 (d) 48
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 5 (d) 3
  8. 8.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
  9. 9.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 136 (c) 126 (d) 135
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  11. 11.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 244 (c) 243 (d) 234
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 5 (d) 15
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  14. 14.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) 72 (b) 24 (c) 27 (d) 8
  15. 15.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 62 (d) 61
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  17. 17.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 255 (c) 246 (d) 242
  18. 18.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) 63 (b) 60 (c) 180 (d) 20
  19. 19.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) 39 (b) 108 (c) 12 (d) 36
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 5 (b) 10 (c) 11 (d) 8
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 20 (d) 19
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 13 (b) 12 (c) 10 (d) 7
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 13 (c) 3 (d) 14
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 20 (d) 19
  25. 25.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 316 (c) 367 (d) 366
  26. 26.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 344 (c) 399 (d) 409
  27. 27.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 166 (c) 176 (d) 175
  28. 28.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 124 (c) 133 (d) 142
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  31. 31.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 106 (c) 96 (d) 105
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 1 (d) 4
  34. 34.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
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 2 (b) 5 (c) 4 (d) 3
  37. 37.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 260 (c) 273 (d) 283
  38. 38.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) 18 (b) 57 (c) 54 (d) 162
  39. 39.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 130 (c) 129 (d) 138
  40. 40.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 65 (c) 74 (d) 66

Answer key

  1. 258
  2. 2
  3. 5
  4. 18
  5. 7
  6. 45
  7. 5
  8. 27
  9. 135
  10. 9
  11. 243
  12. 16
  13. 8
  14. 24
  15. 61
  16. 2
  17. 255
  18. 60
  19. 36
  20. 10
  21. 20
  22. 12
  23. 14
  24. 19
  25. 366
  26. 408
  27. 175
  28. 133
  29. 6
  30. 3
  31. 105
  32. 9
  33. 3
  34. 69
  35. 3
  36. 4
  37. 282
  38. 54
  39. 129
  40. 65

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