← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 394 · 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 times is the digit 9 written when you write all the numbers from 1 to 58? (a) 5 (b) 3 (c) 4 (d) 6
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 17 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  7. 7.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 240 (c) 250 (d) 249
  8. 8.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) 72 (b) 8 (c) 27 (d) 24
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 20 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  12. 12.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 110 (d) 119
  13. 13.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  14. 14.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) 51 (d) 54
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 17 (c) 16 (d) 5
  16. 16.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 142 (c) 151 (d) 160
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 17 (b) 19 (c) 18 (d) 7
  18. 18.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) 69 (b) 72 (c) 23 (d) 207
  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) 69 (b) 22 (c) 66 (d) 198
  20. 20.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 422 (c) 526 (d) 525
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  22. 22.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 490 (c) 627 (d) 618
  23. 23.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 465 (c) 475 (d) 474
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 15 (b) 16 (c) 5 (d) 14
  25. 25.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) 90 (c) 10 (d) 33
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 4 (d) 5
  27. 27.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 492 (c) 621 (d) 630
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 13 (d) 14
  29. 29.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 321 (c) 312 (d) 322
  30. 30.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) 7 (b) 21 (c) 63 (d) 24
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 14 (d) 4
  32. 32.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 373 (c) 363 (d) 320
  33. 33.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 106 (c) 96 (d) 105
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 4 (d) 14
  35. 35.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) 21 (b) 18 (c) 6 (d) 54
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 8 (c) 16 (d) 15
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
  38. 38.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 140 (c) 150 (d) 149
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 9 (b) 17 (c) 18 (d) 15

Answer key

  1. 5
  2. 16
  3. 9
  4. 4
  5. 3
  6. 20
  7. 249
  8. 24
  9. 19
  10. 7
  11. 8
  12. 119
  13. 4
  14. 51
  15. 16
  16. 151
  17. 18
  18. 69
  19. 66
  20. 525
  21. 3
  22. 627
  23. 474
  24. 15
  25. 30
  26. 4
  27. 630
  28. 13
  29. 321
  30. 21
  31. 15
  32. 372
  33. 105
  34. 14
  35. 18
  36. 15
  37. 5
  38. 149
  39. 4
  40. 17

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