← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 41 · 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 two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  3. 3.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) 57 (b) 171 (c) 19 (d) 60
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 17 (d) 18
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 15 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  8. 8.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 76 (c) 85 (d) 94
  9. 9.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 147 (c) 138 (d) 148
  10. 10.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 375 (c) 328 (d) 385
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 17 (d) 18
  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) 51 (b) 16 (c) 48 (d) 144
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 16 (c) 14 (d) 15
  16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 294 (c) 303 (d) 304
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 13 (b) 14 (c) 4 (d) 15
  18. 18.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 568 (c) 567 (d) 558
  19. 19.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) 45 (b) 18 (c) 5 (d) 15
  20. 20.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) 45 (c) 135 (d) 48
  21. 21.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 396 (c) 477 (d) 486
  22. 22.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) 72 (c) 75 (d) 24
  23. 23.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) 30 (b) 33 (c) 10 (d) 90
  24. 24.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) 33 (c) 99 (d) 36
  25. 25.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 364 (d) 439
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20
  28. 28.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) 54 (b) 57 (c) 18 (d) 162
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 5
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 10 (c) 5 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  33. 33.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) 39 (c) 12 (d) 36
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 5 (d) 17
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 1
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  38. 38.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 314 (c) 354 (d) 364
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 5 (d) 2
  40. 40.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 108 (c) 90 (d) 99

Answer key

  1. 8
  2. 2
  3. 57
  4. 18
  5. 16
  6. 5
  7. 5
  8. 85
  9. 147
  10. 384
  11. 15
  12. 4
  13. 18
  14. 48
  15. 15
  16. 303
  17. 14
  18. 567
  19. 15
  20. 45
  21. 486
  22. 72
  23. 30
  24. 33
  25. 438
  26. 18
  27. 20
  28. 54
  29. 4
  30. 19
  31. 9
  32. 4
  33. 36
  34. 18
  35. 16
  36. 3
  37. 3
  38. 363
  39. 4
  40. 99

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