← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 853 · 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 13? (a) 7 (b) 6 (c) 14 (d) 5
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 3 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  4. 4.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) 75 (c) 72 (d) 216
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  6. 6.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
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 20 (c) 19 (d) 9
  8. 8.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 639 (c) 498 (d) 640
  9. 9.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
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 3 (d) 4
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 13 (c) 15 (d) 14
  12. 12.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 390 (c) 478 (d) 468
  13. 13.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) 63 (b) 7 (c) 21 (d) 24
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 21 (d) 19
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
  17. 17.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 615 (d) 482
  18. 18.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) 30 (b) 27 (c) 81 (d) 9
  19. 19.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 150 (c) 149 (d) 158
  20. 20.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 423 (c) 424 (d) 414
  21. 21.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) 54 (c) 51 (d) 17
  22. 22.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) 144 (d) 48
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 19 (d) 17
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 19 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  28. 28.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) 198 (b) 22 (c) 66 (d) 69
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 7 (c) 3 (d) 6
  31. 31.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 489 (c) 498 (d) 499
  32. 32.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) 54 (c) 57 (d) 162
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
  34. 34.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 316 (c) 306 (d) 282
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 17 (d) 5
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 7 (b) 8 (c) 5 (d) 6
  38. 38.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) 33 (b) 30 (c) 10 (d) 90
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 18 (d) 17
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 17 (d) 18

Answer key

  1. 6
  2. 14
  3. 8
  4. 72
  5. 6
  6. 15
  7. 20
  8. 639
  9. 57
  10. 4
  11. 14
  12. 477
  13. 21
  14. 8
  15. 20
  16. 14
  17. 615
  18. 27
  19. 149
  20. 423
  21. 51
  22. 48
  23. 3
  24. 18
  25. 19
  26. 7
  27. 7
  28. 66
  29. 5
  30. 6
  31. 498
  32. 54
  33. 18
  34. 315
  35. 3
  36. 16
  37. 7
  38. 30
  39. 17
  40. 18

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