← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 179 · 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 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 210 (c) 201 (d) 212
  2. 2.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 459 (d) 378
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 20 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  5. 5.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) 13 (b) 42 (c) 39 (d) 117
  6. 6.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) 207 (c) 69 (d) 23
  7. 7.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 550 (c) 438 (d) 540
  8. 8.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 544 (c) 534 (d) 434
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  12. 12.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) 57 (b) 171 (c) 19 (d) 60
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 17 (d) 6
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 15 (d) 16
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 17 (d) 16
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  19. 19.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) 6 (b) 18 (c) 54 (d) 21
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 17 (b) 15 (c) 16 (d) 5
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 4 (d) 2
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 13 (d) 15
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 14 (d) 4
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 16 (d) 15
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 18 (d) 19
  28. 28.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 366 (c) 376 (d) 322
  29. 29.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) 589 (c) 588 (d) 579
  30. 30.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 441 (c) 451 (d) 372
  31. 31.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 643 (c) 642 (d) 633
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 3 (c) 2 (d) 4
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 15 (b) 16 (c) 9 (d) 13
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
  35. 35.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) 39 (d) 36
  36. 36.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) 33 (b) 90 (c) 10 (d) 30
  37. 37.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) 162 (b) 54 (c) 18 (d) 57
  38. 38.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) 216 (c) 72 (d) 24
  39. 39.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) 21 (d) 63
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3

Answer key

  1. 210
  2. 459
  3. 20
  4. 5
  5. 39
  6. 69
  7. 549
  8. 543
  9. 2
  10. 8
  11. 6
  12. 57
  13. 17
  14. 15
  15. 9
  16. 3
  17. 17
  18. 8
  19. 18
  20. 16
  21. 3
  22. 9
  23. 4
  24. 14
  25. 15
  26. 15
  27. 19
  28. 375
  29. 588
  30. 450
  31. 642
  32. 4
  33. 15
  34. 3
  35. 36
  36. 30
  37. 54
  38. 72
  39. 21
  40. 2

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