← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 567 · 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.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 8 (b) 9 (c) 6 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 5 (d) 3
  4. 4.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 394 (c) 474 (d) 484
  5. 5.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) 45 (b) 15 (c) 5 (d) 18
  6. 6.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 429 (c) 439 (d) 364
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  8. 8.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
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 6 (b) 4 (c) 5 (d) 7
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 15 (d) 16
  11. 11.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 406 (c) 502 (d) 501
  12. 12.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) 69 (c) 72 (d) 23
  13. 13.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) 24 (c) 21 (d) 7
  14. 14.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 59 (d) 60
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 3 (d) 10
  18. 18.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) 19 (b) 171 (c) 60 (d) 57
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 5 (d) 6
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 18 (d) 20
  22. 22.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 57 (c) 48 (d) 66
  23. 23.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) 54 (b) 51 (c) 153 (d) 17
  24. 24.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) 20 (b) 180 (c) 63 (d) 60
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 5 (d) 14
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  27. 27.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) 54 (b) 21 (c) 18 (d) 6
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  30. 30.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
  31. 31.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) 21 (c) 66 (d) 189
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  33. 33.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 498 (c) 507 (d) 508
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  35. 35.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) 99 (b) 33 (c) 36 (d) 11
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 6 (b) 18 (c) 17 (d) 16
  37. 37.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 309 (c) 319 (d) 318
  38. 38.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 474 (c) 465 (d) 388
  39. 39.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) 144 (b) 16 (c) 51 (d) 48
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7

Answer key

  1. 8
  2. 5
  3. 5
  4. 483
  5. 15
  6. 438
  7. 3
  8. 42
  9. 6
  10. 15
  11. 501
  12. 69
  13. 21
  14. 59
  15. 8
  16. 4
  17. 10
  18. 57
  19. 9
  20. 6
  21. 19
  22. 57
  23. 51
  24. 60
  25. 15
  26. 18
  27. 18
  28. 9
  29. 20
  30. 255
  31. 63
  32. 6
  33. 507
  34. 3
  35. 33
  36. 17
  37. 318
  38. 474
  39. 48
  40. 7

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