← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 680 · 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 4? (a) 5 (b) 10 (c) 3 (d) 4
  2. 2.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) 66 (c) 198 (d) 22
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  5. 5.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 255 (c) 265 (d) 264
  6. 6.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 546 (c) 555 (d) 556
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 18 (c) 17 (d) 16
  9. 9.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) 15 (d) 5
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 16 (d) 4
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 19 (b) 20 (c) 8 (d) 18
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  13. 13.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 62 (c) 72 (d) 71
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 17 (c) 5 (d) 15
  15. 15.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 78 (d) 87
  16. 16.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) 11 (d) 33
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  19. 19.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 118 (c) 100 (d) 110
  20. 20.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 327 (d) 336
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 17 (d) 16
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 1 (d) 4
  23. 23.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 124 (c) 114 (d) 132
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  26. 26.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 102 (d) 94
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 17 (d) 18
  28. 28.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) 444 (d) 374
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  30. 30.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) 6 (c) 21 (d) 54
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  32. 32.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) 75 (c) 24 (d) 72
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 20 (b) 8 (c) 19 (d) 18
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  35. 35.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 570 (c) 458 (d) 580
  36. 36.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 468 (c) 585 (d) 595
  37. 37.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 231 (d) 232
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 5 (d) 4
  39. 39.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 636 (b) 496 (c) 627 (d) 637
  40. 40.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 322 (c) 376 (d) 375

Answer key

  1. 4
  2. 66
  3. 6
  4. 17
  5. 264
  6. 555
  7. 3
  8. 17
  9. 15
  10. 15
  11. 19
  12. 20
  13. 71
  14. 16
  15. 87
  16. 33
  17. 5
  18. 8
  19. 109
  20. 336
  21. 17
  22. 3
  23. 123
  24. 19
  25. 4
  26. 93
  27. 17
  28. 453
  29. 5
  30. 18
  31. 2
  32. 72
  33. 19
  34. 16
  35. 579
  36. 594
  37. 231
  38. 6
  39. 636
  40. 375

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