← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 906 · 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 2? (a) 3 (b) 2 (c) 1 (d) 10
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 8 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 14 (b) 13 (c) 12 (d) 3
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  6. 6.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 276 (d) 297
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  8. 8.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 529 (c) 424 (d) 519
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 18 (b) 17 (c) 8 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 6 (b) 5 (c) 7 (d) 8
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  14. 14.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) 207 (b) 23 (c) 69 (d) 72
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  16. 16.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 362 (c) 426 (d) 435
  17. 17.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 565 (c) 448 (d) 555
  18. 18.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) 30 (c) 10 (d) 33
  19. 19.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 310 (c) 357 (d) 348
  20. 20.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) 8 (b) 27 (c) 72 (d) 24
  21. 21.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) 24 (d) 75
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  23. 23.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 444 (c) 454 (d) 453
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 3 (d) 12
  25. 25.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) 171 (b) 57 (c) 19 (d) 60
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 2 (d) 3
  27. 27.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 134 (c) 124 (d) 133
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  30. 30.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 61 (c) 52 (d) 62
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 16 (d) 15
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  33. 33.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) 21 (c) 7 (d) 24
  34. 34.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 58 (d) 48
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 1 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 14 (d) 15
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 15 (b) 4 (c) 13 (d) 14
  39. 39.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) 57 (c) 54 (d) 162
  40. 40.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 104 (c) 113 (d) 122

Answer key

  1. 2
  2. 19
  3. 3
  4. 13
  5. 20
  6. 306
  7. 7
  8. 528
  9. 5
  10. 18
  11. 6
  12. 7
  13. 3
  14. 69
  15. 5
  16. 435
  17. 564
  18. 30
  19. 357
  20. 24
  21. 72
  22. 2
  23. 453
  24. 13
  25. 57
  26. 4
  27. 133
  28. 5
  29. 6
  30. 61
  31. 16
  32. 17
  33. 21
  34. 57
  35. 3
  36. 4
  37. 14
  38. 14
  39. 54
  40. 113

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