← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 737 · 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.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 18 (d) 16
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  3. 3.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 124 (c) 133 (d) 142
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 3 (d) 15
  5. 5.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) 18 (b) 54 (c) 21 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  7. 7.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 154 (c) 162 (d) 144
  8. 8.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 74 (c) 66 (d) 65
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 21
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  11. 11.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 41 (d) 50
  12. 12.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 19 (d) 7
  14. 14.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 438 (c) 447 (d) 448
  15. 15.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) 11 (c) 99 (d) 33
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 3 (d) 4
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 14 (d) 4
  18. 18.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 143 (c) 144 (d) 152
  19. 19.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) 340 (c) 330 (d) 298
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  21. 21.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 106 (c) 124 (d) 116
  22. 22.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) 17 (b) 51 (c) 54 (d) 153
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  24. 24.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) 126 (b) 45 (c) 14 (d) 42
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 16 (b) 6 (c) 15 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  28. 28.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 630 (c) 492 (d) 621
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 19 (d) 17
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  31. 31.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
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 13 (d) 14
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  34. 34.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) 492 (c) 483 (d) 400
  35. 35.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) 90 (c) 33 (d) 30
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  37. 37.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 72 (c) 54 (d) 63
  38. 38.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 454 (c) 453 (d) 444
  39. 39.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) 66 (b) 21 (c) 63 (d) 189
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15

Answer key

  1. 17
  2. 5
  3. 133
  4. 14
  5. 18
  6. 4
  7. 153
  8. 65
  9. 20
  10. 3
  11. 41
  12. 9
  13. 18
  14. 447
  15. 33
  16. 3
  17. 15
  18. 143
  19. 339
  20. 4
  21. 115
  22. 51
  23. 8
  24. 42
  25. 3
  26. 16
  27. 6
  28. 630
  29. 18
  30. 15
  31. 21
  32. 14
  33. 2
  34. 492
  35. 30
  36. 5
  37. 63
  38. 453
  39. 63
  40. 15

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