← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 872 · 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 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 592 (c) 591 (d) 582
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 16
  3. 3.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 60 (d) 63
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 19 (c) 16 (d) 9
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  6. 6.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 41 (d) 50
  7. 7.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) 72 (b) 27 (c) 24 (d) 8
  8. 8.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
  9. 9.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 107 (d) 108
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  12. 12.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
  13. 13.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 324 (d) 378
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 18 (d) 20
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  17. 17.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
  18. 18.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 56 (c) 38 (d) 48
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  20. 20.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) 339 (d) 348
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  22. 22.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) 66 (b) 22 (c) 69 (d) 198
  23. 23.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 394 (c) 484 (d) 483
  24. 24.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 190 (c) 172 (d) 181
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 6 (c) 3 (d) 5
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 18 (d) 16
  27. 27.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 288 (c) 264 (d) 289
  28. 28.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 238 (c) 230 (d) 237
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 4 (d) 5
  31. 31.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) 54 (b) 6 (c) 21 (d) 18
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 7 (b) 6 (c) 5 (d) 8
  33. 33.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 138 (c) 148 (d) 147
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 3 (c) 15 (d) 14
  35. 35.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
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  37. 37.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
  38. 38.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 103 (c) 104 (d) 94
  39. 39.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 633 (c) 500 (d) 642
  40. 40.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) 13 (b) 39 (c) 42 (d) 117

Answer key

  1. 591
  2. 17
  3. 60
  4. 18
  5. 8
  6. 41
  7. 24
  8. 48
  9. 107
  10. 3
  11. 2
  12. 300
  13. 378
  14. 19
  15. 9
  16. 4
  17. 10
  18. 47
  19. 8
  20. 348
  21. 7
  22. 66
  23. 483
  24. 181
  25. 5
  26. 17
  27. 288
  28. 237
  29. 6
  30. 5
  31. 18
  32. 7
  33. 147
  34. 14
  35. 57
  36. 6
  37. 36
  38. 103
  39. 642
  40. 39

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