← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 871 · 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 5? (a) 4 (b) 10 (c) 6 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  3. 3.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
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  6. 6.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 495 (c) 504 (d) 505
  7. 7.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) 17 (b) 153 (c) 54 (d) 51
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 15 (d) 16
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 3 (b) 4 (c) 6 (d) 5
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 10 (b) 4 (c) 9 (d) 11
  11. 11.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 454 (c) 374 (d) 444
  12. 12.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  13. 13.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 333 (d) 334
  14. 14.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) 24 (b) 7 (c) 63 (d) 21
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 14 (d) 13
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 18 (d) 19
  17. 17.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 90 (c) 100 (d) 99
  18. 18.The numbers 2 to 10 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) 21 (c) 54 (d) 6
  19. 19.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) 36 (b) 99 (c) 33 (d) 11
  20. 20.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 92 (c) 102 (d) 110
  21. 21.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 376 (c) 366 (d) 322
  22. 22.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) 5 (c) 15 (d) 45
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 14 (c) 3 (d) 13
  24. 24.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 582 (d) 460
  25. 25.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
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  28. 28.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 241 (d) 240
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 5 (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) 150 (b) 158 (c) 140 (d) 149
  32. 32.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 133 (c) 142 (d) 124
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 17 (d) 5
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 21 (d) 20
  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) 48 (b) 51 (c) 144 (d) 16
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  39. 39.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 90 (c) 98 (d) 80
  40. 40.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) 15 (c) 48 (d) 45

Answer key

  1. 5
  2. 8
  3. 69
  4. 4
  5. 9
  6. 504
  7. 51
  8. 16
  9. 5
  10. 10
  11. 453
  12. 9
  13. 333
  14. 21
  15. 14
  16. 19
  17. 99
  18. 18
  19. 33
  20. 101
  21. 375
  22. 15
  23. 14
  24. 582
  25. 72
  26. 7
  27. 8
  28. 240
  29. 20
  30. 4
  31. 149
  32. 133
  33. 16
  34. 19
  35. 20
  36. 48
  37. 3
  38. 6
  39. 89
  40. 45

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