← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 586 · 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 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) 54 (c) 18 (d) 21
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 18 (d) 7
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 19 (d) 18
  4. 4.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 152 (c) 170 (d) 161
  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) 15 (b) 18 (c) 45 (d) 5
  6. 6.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) 216 (b) 24 (c) 75 (d) 72
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 15 (d) 16
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  9. 9.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) 54 (c) 17 (d) 153
  10. 10.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) 10 (b) 30 (c) 90 (d) 33
  11. 11.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 543 (c) 534 (d) 434
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  13. 13.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 338 (c) 400 (d) 399
  14. 14.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) 16 (b) 48 (c) 144 (d) 51
  15. 15.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 567 (c) 568 (d) 450
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  17. 17.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 579 (d) 588
  18. 18.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) 14 (b) 126 (c) 42 (d) 45
  19. 19.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 100 (c) 109 (d) 110
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 14 (c) 3 (d) 15
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 18 (d) 19
  22. 22.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) 63 (c) 21 (d) 24
  23. 23.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 631 (c) 621 (d) 630
  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) 60 (b) 20 (c) 63 (d) 180
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 5 (b) 2 (c) 3 (d) 4
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 8 (d) 20
  27. 27.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) 198 (b) 69 (c) 22 (d) 66
  28. 28.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) 108 (b) 36 (c) 12 (d) 39
  29. 29.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
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 8 (d) 18
  31. 31.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) 117 (d) 39
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 6 (d) 17
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 15 (c) 8 (d) 13
  34. 34.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) 135 (c) 48 (d) 45
  35. 35.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 152 (c) 151 (d) 142
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  37. 37.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 87 (c) 96 (d) 78
  38. 38.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 520 (d) 519
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  40. 40.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) 24 (b) 8 (c) 27 (d) 72

Answer key

  1. 18
  2. 17
  3. 19
  4. 161
  5. 15
  6. 72
  7. 15
  8. 17
  9. 51
  10. 30
  11. 543
  12. 5
  13. 399
  14. 48
  15. 567
  16. 19
  17. 588
  18. 42
  19. 109
  20. 14
  21. 19
  22. 21
  23. 630
  24. 60
  25. 4
  26. 19
  27. 66
  28. 36
  29. 54
  30. 18
  31. 39
  32. 17
  33. 15
  34. 45
  35. 151
  36. 20
  37. 87
  38. 519
  39. 4
  40. 24

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