← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 638 · 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.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) 30 (c) 10 (d) 33
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 16
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  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) 27 (b) 8 (c) 24 (d) 72
  8. 8.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) 24 (d) 216
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 17 (d) 19
  10. 10.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 339 (c) 349 (d) 348
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
  12. 12.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 80 (c) 89 (d) 90
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  14. 14.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 601 (c) 472 (d) 600
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  16. 16.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 183 (c) 192 (d) 174
  17. 17.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) 18 (b) 21 (c) 6 (d) 54
  18. 18.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 148 (c) 140 (d) 139
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  20. 20.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 23 (d) 69
  21. 21.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) 117 (b) 39 (c) 13 (d) 42
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 17 (c) 7 (d) 19
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 5 (b) 6 (c) 4 (d) 3
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 17 (d) 5
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  27. 27.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) 51 (b) 48 (c) 16 (d) 144
  28. 28.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 60 (d) 59
  29. 29.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 438 (c) 549 (d) 550
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 18
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 19 (d) 18
  32. 32.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 504 (d) 495
  33. 33.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 100 (c) 90 (d) 108
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 2 (d) 1
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 6 (b) 8 (c) 9 (d) 7
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  38. 38.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 244 (c) 351 (d) 234
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  40. 40.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) 60 (c) 57 (d) 19

Answer key

  1. 30
  2. 4
  3. 6
  4. 17
  5. 3
  6. 4
  7. 24
  8. 72
  9. 18
  10. 348
  11. 18
  12. 89
  13. 5
  14. 600
  15. 9
  16. 183
  17. 18
  18. 139
  19. 7
  20. 69
  21. 39
  22. 3
  23. 18
  24. 5
  25. 16
  26. 17
  27. 48
  28. 59
  29. 549
  30. 19
  31. 19
  32. 504
  33. 99
  34. 3
  35. 8
  36. 5
  37. 2
  38. 243
  39. 8
  40. 57

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