← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 260 · 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 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 396 (c) 342 (d) 406
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  4. 4.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 116 (c) 106 (d) 124
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  6. 6.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) 22 (c) 69 (d) 66
  7. 7.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 440 (c) 543 (d) 553
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 3 (d) 5
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 8 (b) 7 (c) 3 (d) 9
  11. 11.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 74 (c) 66 (d) 56
  12. 12.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 274 (c) 304 (d) 303
  13. 13.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 360 (c) 370 (d) 369
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 5 (d) 14
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 6 (d) 5
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 18
  18. 18.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 258 (c) 268 (d) 250
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  20. 20.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 218 (c) 219 (d) 210
  21. 21.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) 72 (b) 75 (c) 216 (d) 24
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 6 (d) 4
  23. 23.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 187 (c) 196 (d) 178
  24. 24.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 202 (c) 195 (d) 186
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  26. 26.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) 12 (b) 39 (c) 108 (d) 36
  27. 27.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) 15 (c) 45 (d) 135
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 14 (c) 13 (d) 4
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 16 (d) 15
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 5 (d) 4
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 6 (b) 4 (c) 5 (d) 7
  32. 32.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 304 (c) 348 (d) 339
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  34. 34.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 612 (c) 480 (d) 603
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
  36. 36.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 124 (d) 123
  37. 37.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 97 (c) 106 (d) 98
  38. 38.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) 18 (c) 54 (d) 162
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 16 (d) 6

Answer key

  1. 405
  2. 5
  3. 8
  4. 115
  5. 20
  6. 66
  7. 552
  8. 4
  9. 15
  10. 8
  11. 65
  12. 303
  13. 369
  14. 6
  15. 6
  16. 5
  17. 19
  18. 267
  19. 15
  20. 219
  21. 72
  22. 5
  23. 187
  24. 195
  25. 4
  26. 36
  27. 45
  28. 14
  29. 16
  30. 4
  31. 6
  32. 348
  33. 9
  34. 612
  35. 17
  36. 123
  37. 97
  38. 54
  39. 18
  40. 16

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