← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 82 · 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 16? (a) 3 (b) 4 (c) 2 (d) 17
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 12 (c) 13 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  4. 4.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) 57 (b) 162 (c) 18 (d) 54
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 19 (d) 18
  6. 6.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 135 (d) 136
  7. 7.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 134 (c) 133 (d) 142
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 9 (c) 5 (d) 6
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 16 (d) 7
  11. 11.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) 10 (c) 30 (d) 33
  12. 12.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) 320 (d) 363
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 3 (d) 1
  14. 14.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) 75 (b) 24 (c) 72 (d) 216
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  16. 16.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 426 (d) 427
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 3 (d) 1
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 5 (d) 17
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  20. 20.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 474 (d) 394
  21. 21.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) 135 (b) 48 (c) 45 (d) 15
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  23. 23.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) 555 (c) 556 (d) 546
  24. 24.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 187 (c) 188 (d) 196
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  26. 26.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) 198 (b) 66 (c) 69 (d) 22
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 18 (d) 19
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 17 (b) 5 (c) 15 (d) 16
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 2 (d) 3
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 6 (d) 15
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  33. 33.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 346 (c) 411 (d) 412
  34. 34.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) 45 (b) 5 (c) 18 (d) 15
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  36. 36.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 129 (c) 120 (d) 130
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 6 (d) 3
  38. 38.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 83 (c) 92 (d) 84
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  40. 40.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 351 (c) 361 (d) 360

Answer key

  1. 3
  2. 12
  3. 7
  4. 54
  5. 18
  6. 135
  7. 133
  8. 8
  9. 20
  10. 17
  11. 30
  12. 372
  13. 3
  14. 72
  15. 5
  16. 426
  17. 3
  18. 16
  19. 8
  20. 483
  21. 45
  22. 7
  23. 555
  24. 187
  25. 6
  26. 66
  27. 17
  28. 19
  29. 16
  30. 4
  31. 16
  32. 18
  33. 411
  34. 15
  35. 6
  36. 129
  37. 5
  38. 83
  39. 5
  40. 360

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