← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 594 · 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.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) 18 (b) 57 (c) 162 (d) 54
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 7 (b) 10 (c) 13 (d) 12
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  5. 5.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) 23 (b) 69 (c) 72 (d) 207
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 14 (c) 4 (d) 15
  7. 7.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 565 (d) 564
  8. 8.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 616 (c) 482 (d) 606
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  11. 11.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 432 (c) 441 (d) 366
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 4 (d) 6
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 2 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 6 (d) 18
  17. 17.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 603 (d) 612
  18. 18.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) 51 (c) 54 (d) 17
  19. 19.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 158 (d) 168
  20. 20.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 486 (c) 496 (d) 495
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
  22. 22.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 231 (c) 240 (d) 232
  23. 23.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
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 3 (d) 2
  25. 25.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) 63 (c) 180 (d) 60
  26. 26.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) 246 (c) 242 (d) 256
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  30. 30.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) 8 (c) 24 (d) 72
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 9 (d) 19
  33. 33.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 80 (d) 79
  34. 34.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) 414 (c) 504 (d) 513
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 6 (d) 3
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 6 (b) 4 (c) 7 (d) 5
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
  40. 40.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 435 (c) 368 (d) 445

Answer key

  1. 54
  2. 12
  3. 2
  4. 6
  5. 69
  6. 15
  7. 564
  8. 615
  9. 2
  10. 8
  11. 441
  12. 5
  13. 4
  14. 7
  15. 20
  16. 17
  17. 612
  18. 51
  19. 167
  20. 495
  21. 3
  22. 240
  23. 372
  24. 4
  25. 60
  26. 255
  27. 18
  28. 18
  29. 7
  30. 24
  31. 15
  32. 20
  33. 79
  34. 513
  35. 9
  36. 3
  37. 5
  38. 6
  39. 16
  40. 444

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