← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 763 · 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 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 262 (c) 252 (d) 261
  2. 2.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 394 (d) 474
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 10 (d) 9
  4. 4.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) 72 (b) 23 (c) 69 (d) 207
  5. 5.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 636 (c) 496 (d) 627
  6. 6.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 69 (c) 198 (d) 22
  7. 7.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
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 9 (d) 20
  9. 9.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 214 (c) 321 (d) 213
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 4 (d) 15
  11. 11.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) 15 (b) 48 (c) 45 (d) 135
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  13. 13.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) 18 (c) 6 (d) 21
  14. 14.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 460 (d) 459
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  16. 16.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) 45 (d) 42
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 5 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  19. 19.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) 51 (c) 48 (d) 16
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 3 (d) 6
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 18 (d) 17
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  23. 23.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 314 (c) 363 (d) 364
  24. 24.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 256 (c) 242 (d) 246
  25. 25.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 495 (d) 504
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  28. 28.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 501 (c) 406 (d) 492
  29. 29.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) 45 (d) 5
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 15 (b) 4 (c) 14 (d) 16
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 6 (b) 9 (c) 7 (d) 10
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 17 (d) 19
  33. 33.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) 27 (b) 24 (c) 8 (d) 72
  34. 34.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) 318 (d) 319
  35. 35.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) 51 (b) 17 (c) 153 (d) 54
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 21 (b) 20 (c) 19 (d) 9
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 16 (c) 15 (d) 8
  38. 38.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 609 (c) 484 (d) 618
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 18 (d) 8
  40. 40.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 504 (c) 513 (d) 414

Answer key

  1. 261
  2. 483
  3. 9
  4. 69
  5. 636
  6. 66
  7. 27
  8. 20
  9. 213
  10. 15
  11. 45
  12. 9
  13. 18
  14. 459
  15. 5
  16. 42
  17. 5
  18. 6
  19. 48
  20. 5
  21. 18
  22. 8
  23. 363
  24. 255
  25. 504
  26. 3
  27. 20
  28. 501
  29. 15
  30. 15
  31. 9
  32. 18
  33. 24
  34. 318
  35. 51
  36. 20
  37. 15
  38. 618
  39. 19
  40. 513

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