← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 929 · 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 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 249 (d) 238
  2. 2.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) 33 (c) 90 (d) 30
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  6. 6.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 368 (d) 444
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 9 (c) 12 (d) 11
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  10. 10.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 464 (c) 589 (d) 588
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  12. 12.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 61 (c) 62 (d) 52
  13. 13.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 487 (c) 396 (d) 477
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  15. 15.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) 7 (c) 24 (d) 63
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 21
  17. 17.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 382 (c) 372 (d) 381
  18. 18.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) 18 (b) 45 (c) 5 (d) 15
  19. 19.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) 22 (b) 198 (c) 69 (d) 66
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 11 (b) 7 (c) 10 (d) 8
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  24. 24.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) 27 (b) 8 (c) 24 (d) 72
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  26. 26.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) 24 (b) 216 (c) 75 (d) 72
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 16 (d) 17
  28. 28.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) 117 (b) 39 (c) 42 (d) 13
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 6 (d) 3
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 16 (c) 6 (d) 17
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 2 (d) 4
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 17 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 5 (d) 15
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  36. 36.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) 51 (d) 144
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  38. 38.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 95 (c) 96 (d) 86
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  40. 40.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) 11 (b) 99 (c) 36 (d) 33

Answer key

  1. 249
  2. 30
  3. 2
  4. 4
  5. 9
  6. 444
  7. 3
  8. 11
  9. 8
  10. 588
  11. 3
  12. 61
  13. 486
  14. 9
  15. 21
  16. 20
  17. 381
  18. 15
  19. 66
  20. 7
  21. 10
  22. 19
  23. 4
  24. 24
  25. 6
  26. 72
  27. 16
  28. 39
  29. 5
  30. 16
  31. 3
  32. 18
  33. 7
  34. 16
  35. 18
  36. 48
  37. 6
  38. 95
  39. 19
  40. 33

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