← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 744 · 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 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) 21 (b) 24 (c) 63 (d) 7
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 16 (d) 17
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 18 (d) 9
  4. 4.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) 189 (b) 21 (c) 66 (d) 63
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 2 (d) 3
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 16 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  8. 8.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 298 (c) 330 (d) 340
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  10. 10.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 60 (d) 50
  11. 11.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) 39 (b) 36 (c) 108 (d) 12
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  14. 14.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 83 (d) 84
  15. 15.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 384 (c) 468 (d) 469
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  17. 17.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) 30 (d) 10
  18. 18.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 439 (b) 429 (c) 438 (d) 364
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 4 (b) 7 (c) 6 (d) 5
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 6 (b) 5 (c) 4 (d) 7
  21. 21.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 56 (d) 65
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 18 (d) 17
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 4 (b) 5 (c) 7 (d) 6
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 3 (d) 2
  27. 27.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) 39 (b) 13 (c) 117 (d) 42
  28. 28.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) 9 (b) 81 (c) 30 (d) 27
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 6 (c) 4 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 20 (d) 8
  32. 32.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 306 (c) 351 (d) 342
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  34. 34.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) 63 (b) 20 (c) 180 (d) 60
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 11 (c) 13 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  37. 37.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 550 (c) 540 (d) 549
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
  39. 39.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 460 (d) 583
  40. 40.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

Answer key

  1. 21
  2. 17
  3. 19
  4. 63
  5. 4
  6. 17
  7. 8
  8. 339
  9. 6
  10. 59
  11. 36
  12. 20
  13. 8
  14. 83
  15. 468
  16. 6
  17. 30
  18. 438
  19. 6
  20. 6
  21. 65
  22. 5
  23. 6
  24. 17
  25. 6
  26. 4
  27. 39
  28. 27
  29. 6
  30. 9
  31. 19
  32. 351
  33. 7
  34. 60
  35. 12
  36. 3
  37. 549
  38. 4
  39. 582
  40. 18

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