← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 957 · 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 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 106 (c) 114 (d) 96
  2. 2.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) 72 (d) 216
  3. 3.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 385 (c) 384 (d) 375
  4. 4.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 357 (c) 366 (d) 367
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  8. 8.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 439 (d) 364
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 19 (c) 17 (d) 7
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  12. 12.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 147 (c) 148 (d) 138
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 7 (b) 6 (c) 8 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  17. 17.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 140 (d) 149
  18. 18.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) 144 (d) 16
  19. 19.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 607 (b) 476 (c) 606 (d) 597
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  21. 21.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 358 (c) 430 (d) 429
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  23. 23.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) 90 (b) 33 (c) 10 (d) 30
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 3 (d) 15
  26. 26.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 228 (c) 234 (d) 225
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 7 (b) 8 (c) 6 (d) 5
  28. 28.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 54 (c) 17 (d) 51
  29. 29.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 89 (c) 80 (d) 90
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 12 (c) 3 (d) 11
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 5 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 14 (d) 15
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 4 (b) 5 (c) 3 (d) 2
  36. 36.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 171 (c) 172 (d) 162
  37. 37.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) 30 (b) 9 (c) 81 (d) 27
  38. 38.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) 39 (b) 13 (c) 42 (d) 117
  39. 39.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 87 (c) 96 (d) 78
  40. 40.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) 14 (c) 42 (d) 45

Answer key

  1. 105
  2. 72
  3. 384
  4. 366
  5. 19
  6. 5
  7. 5
  8. 438
  9. 18
  10. 3
  11. 17
  12. 147
  13. 6
  14. 3
  15. 7
  16. 8
  17. 149
  18. 48
  19. 606
  20. 4
  21. 429
  22. 17
  23. 30
  24. 8
  25. 14
  26. 234
  27. 7
  28. 51
  29. 89
  30. 11
  31. 16
  32. 2
  33. 15
  34. 6
  35. 4
  36. 171
  37. 27
  38. 39
  39. 87
  40. 42

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