← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 803 · 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 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 179 (c) 170 (d) 188
  2. 2.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) 69 (b) 207 (c) 23 (d) 72
  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) 385 (b) 328 (c) 375 (d) 384
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  5. 5.The numbers 17 to 25 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) 66 (c) 189 (d) 21
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 7 (c) 17 (d) 18
  9. 9.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 577 (c) 567 (d) 456
  10. 10.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 112 (c) 104 (d) 103
  11. 11.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 114 (d) 105
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 19 (d) 7
  13. 13.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 120 (c) 128 (d) 119
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 4 (d) 5
  15. 15.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 394 (c) 483 (d) 484
  16. 16.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 579 (c) 589 (d) 588
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 4 (b) 3 (c) 5 (d) 2
  19. 19.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) 45 (b) 42 (c) 126 (d) 14
  20. 20.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
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  23. 23.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) 18 (c) 5 (d) 45
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
  25. 25.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) 12 (b) 108 (c) 36 (d) 39
  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) 399 (c) 344 (d) 409
  27. 27.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) 27 (d) 81
  28. 28.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 558 (d) 567
  29. 29.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 388 (c) 465 (d) 475
  30. 30.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 140 (c) 131 (d) 122
  31. 31.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) 140 (c) 150 (d) 149
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 7 (b) 6 (c) 8 (d) 9
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 3 (d) 5
  36. 36.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 153 (c) 162 (d) 154
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  40. 40.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) 7 (b) 24 (c) 63 (d) 21

Answer key

  1. 179
  2. 69
  3. 384
  4. 3
  5. 63
  6. 6
  7. 18
  8. 18
  9. 576
  10. 103
  11. 105
  12. 18
  13. 119
  14. 5
  15. 483
  16. 588
  17. 9
  18. 4
  19. 42
  20. 45
  21. 4
  22. 5
  23. 15
  24. 17
  25. 36
  26. 408
  27. 27
  28. 567
  29. 474
  30. 131
  31. 149
  32. 9
  33. 8
  34. 8
  35. 4
  36. 153
  37. 19
  38. 6
  39. 7
  40. 21

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