← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 864 · 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 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 252 (c) 253 (d) 243
  2. 2.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) 60 (b) 171 (c) 19 (d) 57
  3. 3.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 421 (c) 420 (d) 411
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  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) 207 (b) 23 (c) 69 (d) 72
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 21
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  8. 8.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) 24 (b) 21 (c) 7 (d) 63
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 15 (d) 17
  12. 12.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 114 (d) 132
  13. 13.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) 36 (b) 12 (c) 108 (d) 39
  14. 14.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 493 (b) 400 (c) 483 (d) 492
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 17 (d) 18
  16. 16.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) 42 (b) 13 (c) 39 (d) 117
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 16 (c) 17 (d) 15
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 5 (d) 14
  19. 19.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 129 (d) 130
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  21. 21.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) 63 (c) 20 (d) 180
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  24. 24.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 523 (d) 420
  25. 25.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) 8 (b) 72 (c) 27 (d) 24
  26. 26.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 99 (d) 11
  27. 27.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
  28. 28.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) 17 (d) 54
  29. 29.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) 30 (c) 27 (d) 81
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 5 (d) 16
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 2 (d) 5
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 4 (d) 5
  36. 36.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 276 (d) 297
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 20 (d) 19
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  39. 39.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
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 6 (d) 16

Answer key

  1. 252
  2. 57
  3. 420
  4. 8
  5. 69
  6. 20
  7. 3
  8. 21
  9. 4
  10. 9
  11. 16
  12. 123
  13. 36
  14. 492
  15. 18
  16. 39
  17. 16
  18. 15
  19. 129
  20. 7
  21. 60
  22. 2
  23. 5
  24. 522
  25. 24
  26. 33
  27. 54
  28. 51
  29. 27
  30. 16
  31. 8
  32. 6
  33. 6
  34. 4
  35. 5
  36. 306
  37. 19
  38. 3
  39. 18
  40. 17

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