← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 381 · 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 times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 12 (d) 13
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  6. 6.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 246 (c) 261 (d) 252
  7. 7.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 538 (c) 528 (d) 430
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 21
  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) 15 (b) 5 (c) 45 (d) 18
  10. 10.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 132 (c) 150 (d) 142
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 15 (d) 16
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 5 (d) 3
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 5 (c) 7 (d) 8
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 17 (d) 8
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 15 (c) 17 (d) 16
  17. 17.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) 427 (c) 426 (d) 417
  18. 18.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 42 (c) 13 (d) 117
  19. 19.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) 16 (b) 144 (c) 48 (d) 51
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  21. 21.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 291 (c) 301 (d) 272
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 5 (b) 2 (c) 4 (d) 3
  23. 23.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 501 (c) 412 (d) 510
  24. 24.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 211 (d) 210
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  26. 26.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 153 (c) 144 (d) 162
  27. 27.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) 22 (c) 198 (d) 66
  28. 28.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 326 (c) 382 (d) 381
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 16 (d) 17
  30. 30.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
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 20 (b) 21 (c) 9 (d) 19
  32. 32.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 185 (c) 186 (d) 176
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
  35. 35.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 42 (c) 45 (d) 14
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  37. 37.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 429 (c) 420 (d) 358
  38. 38.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) 81 (b) 27 (c) 9 (d) 30
  39. 39.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
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 18 (d) 16

Answer key

  1. 13
  2. 2
  3. 4
  4. 7
  5. 5
  6. 261
  7. 537
  8. 20
  9. 15
  10. 141
  11. 15
  12. 5
  13. 3
  14. 7
  15. 18
  16. 16
  17. 426
  18. 39
  19. 48
  20. 5
  21. 300
  22. 4
  23. 510
  24. 210
  25. 7
  26. 153
  27. 66
  28. 381
  29. 16
  30. 72
  31. 20
  32. 185
  33. 6
  34. 19
  35. 42
  36. 4
  37. 429
  38. 27
  39. 16
  40. 17

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