← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 439 · 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 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 4 (c) 5 (d) 6
  2. 2.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) 42 (b) 45 (c) 126 (d) 14
  3. 3.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
  4. 4.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) 30 (b) 90 (c) 33 (d) 10
  5. 5.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 376 (c) 375 (d) 366
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 14 (c) 4 (d) 13
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 2 (d) 4
  8. 8.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 286 (c) 321 (d) 312
  9. 9.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 238 (c) 240 (d) 250
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 15 (d) 16
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 3 (c) 15 (d) 14
  15. 15.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
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 6 (c) 7 (d) 8
  18. 18.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 415 (c) 348 (d) 405
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 6 (b) 7 (c) 5 (d) 8
  20. 20.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 201 (c) 211 (d) 212
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  22. 22.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) 8 (b) 72 (c) 24 (d) 27
  23. 23.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 558 (d) 568
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 11 (b) 14 (c) 13 (d) 7
  25. 25.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 91 (c) 82 (d) 100
  26. 26.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 458 (c) 580 (d) 570
  27. 27.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 17 (c) 153 (d) 54
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 18
  30. 30.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 446 (c) 561 (d) 552
  31. 31.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 5 (d) 15
  33. 33.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 549 (c) 550 (d) 540
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  35. 35.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 160 (d) 159
  36. 36.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 36 (d) 45
  37. 37.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) 6 (b) 54 (c) 18 (d) 21
  38. 38.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 480 (c) 613 (d) 612
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
  40. 40.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 170 (c) 162 (d) 161

Answer key

  1. 6
  2. 42
  3. 66
  4. 30
  5. 375
  6. 14
  7. 4
  8. 321
  9. 249
  10. 8
  11. 3
  12. 15
  13. 5
  14. 14
  15. 133
  16. 9
  17. 8
  18. 414
  19. 7
  20. 210
  21. 8
  22. 24
  23. 567
  24. 13
  25. 91
  26. 579
  27. 51
  28. 6
  29. 19
  30. 561
  31. 7
  32. 16
  33. 549
  34. 19
  35. 159
  36. 45
  37. 18
  38. 612
  39. 19
  40. 161

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