← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 335 · 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 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 414 (d) 348
  2. 2.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 535 (d) 525
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 19 (d) 7
  6. 6.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 316 (c) 282 (d) 306
  7. 7.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) 144 (b) 51 (c) 48 (d) 16
  8. 8.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) 162 (b) 18 (c) 57 (d) 54
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19
  10. 10.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) 21 (c) 63 (d) 7
  11. 11.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) 19 (c) 57 (d) 60
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 7 (d) 17
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 8 (b) 17 (c) 18 (d) 19
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 17 (c) 5 (d) 15
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 19 (d) 8
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
  20. 20.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 81 (d) 30
  21. 21.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 130 (c) 122 (d) 112
  22. 22.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 642 (c) 633 (d) 643
  23. 23.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 52 (d) 60
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  25. 25.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) 72 (b) 23 (c) 69 (d) 207
  26. 26.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) 75 (c) 216 (d) 72
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 16 (c) 5 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  29. 29.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) 48 (b) 135 (c) 45 (d) 15
  30. 30.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 411 (c) 402 (d) 346
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 1 (b) 3 (c) 4 (d) 2
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 4 (b) 10 (c) 9 (d) 11
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  35. 35.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 72 (c) 54 (d) 64
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  37. 37.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 342 (c) 333 (d) 300
  38. 38.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 49 (d) 50
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 9 (d) 20

Answer key

  1. 414
  2. 534
  3. 9
  4. 8
  5. 18
  6. 315
  7. 48
  8. 54
  9. 19
  10. 21
  11. 57
  12. 17
  13. 17
  14. 5
  15. 18
  16. 15
  17. 16
  18. 18
  19. 4
  20. 27
  21. 121
  22. 642
  23. 51
  24. 19
  25. 69
  26. 72
  27. 16
  28. 3
  29. 45
  30. 411
  31. 8
  32. 3
  33. 10
  34. 3
  35. 63
  36. 4
  37. 342
  38. 49
  39. 2
  40. 20

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