← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 917 · 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 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 372 (c) 450 (d) 441
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  5. 5.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 622 (c) 486 (d) 621
  6. 6.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 438 (c) 550 (d) 549
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 3 (d) 6
  8. 8.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 36 (d) 35
  9. 9.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) 81 (b) 30 (c) 9 (d) 27
  10. 10.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) 21 (b) 189 (c) 63 (d) 66
  11. 11.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) 57 (b) 18 (c) 162 (d) 54
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 2 (d) 3
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 18 (d) 19
  16. 16.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  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) 90 (b) 33 (c) 10 (d) 30
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 12 (b) 5 (c) 11 (d) 13
  19. 19.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) 54 (b) 17 (c) 153 (d) 51
  20. 20.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 229 (c) 228 (d) 224
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 18 (d) 17
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 5 (d) 3
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
  26. 26.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 124 (c) 116 (d) 115
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 15 (d) 16
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 18 (b) 17 (c) 8 (d) 19
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 3 (b) 4 (c) 5 (d) 6
  34. 34.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) 7 (d) 63
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  36. 36.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) 135 (b) 45 (c) 15 (d) 48
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 6 (c) 17 (d) 16
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 7 (d) 19
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  40. 40.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327

Answer key

  1. 450
  2. 5
  3. 2
  4. 7
  5. 621
  6. 549
  7. 5
  8. 35
  9. 27
  10. 63
  11. 54
  12. 447
  13. 2
  14. 4
  15. 18
  16. 8
  17. 30
  18. 12
  19. 51
  20. 228
  21. 18
  22. 8
  23. 20
  24. 4
  25. 3
  26. 115
  27. 9
  28. 3
  29. 7
  30. 15
  31. 4
  32. 18
  33. 5
  34. 21
  35. 6
  36. 45
  37. 17
  38. 18
  39. 5
  40. 336

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