← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 472 · 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.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 286 (c) 321 (d) 312
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  3. 3.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 585 (c) 594 (d) 468
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  5. 5.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) 63 (c) 21 (d) 7
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 17 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 5 (d) 4
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 18 (d) 20
  11. 11.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 394 (c) 384 (d) 334
  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) 110 (b) 120 (c) 128 (d) 119
  13. 13.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 36 (d) 39
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 7 (c) 9 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
  17. 17.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 188 (c) 170 (d) 179
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 4 (d) 2
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 4 (d) 13
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 8 (d) 18
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 7 (c) 8 (d) 6
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 13 (d) 3
  26. 26.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) 153 (b) 51 (c) 17 (d) 54
  27. 27.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 528 (c) 537 (d) 430
  28. 28.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 94 (c) 112 (d) 104
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 13 (b) 15 (c) 3 (d) 14
  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.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) 24 (b) 72 (c) 8 (d) 27
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 7 (c) 8 (d) 9
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 14 (b) 13 (c) 5 (d) 12
  36. 36.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 531 (c) 540 (d) 432
  37. 37.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) 24 (b) 216 (c) 75 (d) 72
  38. 38.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) 69 (c) 207 (d) 72
  39. 39.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) 21 (b) 189 (c) 63 (d) 66
  40. 40.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 382 (c) 466 (d) 465

Answer key

  1. 321
  2. 2
  3. 594
  4. 20
  5. 21
  6. 17
  7. 3
  8. 7
  9. 4
  10. 19
  11. 393
  12. 119
  13. 36
  14. 9
  15. 6
  16. 20
  17. 179
  18. 4
  19. 14
  20. 5
  21. 2
  22. 3
  23. 18
  24. 8
  25. 14
  26. 51
  27. 537
  28. 103
  29. 14
  30. 18
  31. 24
  32. 4
  33. 8
  34. 8
  35. 13
  36. 540
  37. 72
  38. 69
  39. 63
  40. 465

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