← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 299 · 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 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 442 (d) 441
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 18 (d) 19
  3. 3.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 330 (c) 298 (d) 340
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 16 (d) 5
  5. 5.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) 63 (b) 21 (c) 24 (d) 7
  6. 6.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 130 (c) 120 (d) 129
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  8. 8.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 633 (c) 494 (d) 624
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 1 (b) 3 (c) 2 (d) 4
  11. 11.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) 175 (c) 176 (d) 166
  12. 12.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) 57 (b) 171 (c) 60 (d) 19
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 6 (b) 5 (c) 7 (d) 8
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 2
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  20. 20.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) 162 (b) 57 (c) 18 (d) 54
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  22. 22.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 150 (d) 141
  23. 23.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) 24 (c) 72 (d) 27
  24. 24.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 26 (c) 36 (d) 44
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  26. 26.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) 33 (b) 11 (c) 36 (d) 99
  27. 27.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) 20 (c) 60 (d) 180
  28. 28.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 268 (c) 250 (d) 258
  29. 29.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 153 (d) 144
  30. 30.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) 15 (b) 5 (c) 45 (d) 18
  31. 31.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 204 (c) 205 (d) 195
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
  33. 33.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 84 (d) 83
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  36. 36.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 320 (c) 373 (d) 363
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 6 (d) 7
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 15 (d) 16
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2

Answer key

  1. 441
  2. 19
  3. 339
  4. 16
  5. 21
  6. 129
  7. 8
  8. 633
  9. 9
  10. 3
  11. 175
  12. 57
  13. 19
  14. 4
  15. 7
  16. 4
  17. 6
  18. 2
  19. 3
  20. 54
  21. 2
  22. 141
  23. 24
  24. 35
  25. 5
  26. 33
  27. 60
  28. 267
  29. 153
  30. 15
  31. 204
  32. 18
  33. 83
  34. 7
  35. 3
  36. 372
  37. 4
  38. 7
  39. 15
  40. 3

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