← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 938 · 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.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 207 (d) 69
  2. 2.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) 48 (b) 51 (c) 144 (d) 16
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  4. 4.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
  5. 5.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) 10 (c) 30 (d) 33
  6. 6.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 627 (c) 618 (d) 628
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 20 (d) 19
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  9. 9.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 288 (d) 325
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  12. 12.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 496 (c) 486 (d) 495
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 5 (d) 3
  14. 14.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 220 (c) 210 (d) 218
  15. 15.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) 45 (b) 42 (c) 126 (d) 14
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 11 (c) 12 (d) 3
  17. 17.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) 66 (b) 22 (c) 69 (d) 198
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  20. 20.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) 99 (b) 11 (c) 33 (d) 36
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  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) 54 (b) 17 (c) 51 (d) 153
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 5 (c) 4 (d) 6
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 5 (d) 2
  25. 25.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 316 (c) 367 (d) 366
  26. 26.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 588 (d) 597
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 2 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 5 (b) 7 (c) 4 (d) 6
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  31. 31.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
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 5 (d) 3
  33. 33.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) 15 (c) 18 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 10 (c) 12 (d) 11
  36. 36.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) 63 (c) 72 (d) 54
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  39. 39.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) 27 (d) 9
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 7 (b) 4 (c) 5 (d) 6

Answer key

  1. 69
  2. 48
  3. 4
  4. 63
  5. 30
  6. 627
  7. 20
  8. 5
  9. 324
  10. 9
  11. 6
  12. 495
  13. 5
  14. 219
  15. 42
  16. 11
  17. 66
  18. 9
  19. 6
  20. 33
  21. 20
  22. 51
  23. 5
  24. 4
  25. 366
  26. 597
  27. 4
  28. 8
  29. 6
  30. 3
  31. 149
  32. 4
  33. 15
  34. 2
  35. 11
  36. 63
  37. 5
  38. 7
  39. 27
  40. 6

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