← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 133 · 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 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) 16 (d) 48
  2. 2.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) 33 (b) 10 (c) 30 (d) 90
  3. 3.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 456 (d) 465
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 21 (d) 20
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  8. 8.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) 9 (b) 27 (c) 81 (d) 30
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  10. 10.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 99 (c) 36 (d) 11
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  12. 12.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 396 (c) 342 (d) 405
  13. 13.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 314 (c) 364 (d) 354
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
  16. 16.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 382 (c) 372 (d) 326
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 13 (c) 11 (d) 7
  18. 18.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) 63 (d) 60
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  20. 20.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) 108 (b) 36 (c) 12 (d) 39
  21. 21.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 564 (d) 565
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 4 (c) 5 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  27. 27.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 595 (d) 594
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
  29. 29.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 265 (c) 248 (d) 255
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 7 (c) 6 (d) 5
  31. 31.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 170 (c) 161 (d) 152
  32. 32.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) 17 (b) 54 (c) 153 (d) 51
  33. 33.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
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
  35. 35.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 228 (c) 219 (d) 229
  36. 36.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 156 (c) 165 (d) 166
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 18 (d) 8
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 6 (b) 7 (c) 4 (d) 5
  39. 39.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) 27 (c) 72 (d) 24
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 17 (c) 18 (d) 7

Answer key

  1. 48
  2. 30
  3. 465
  4. 9
  5. 7
  6. 20
  7. 20
  8. 27
  9. 5
  10. 33
  11. 2
  12. 405
  13. 363
  14. 3
  15. 19
  16. 381
  17. 13
  18. 60
  19. 19
  20. 36
  21. 564
  22. 4
  23. 2
  24. 5
  25. 8
  26. 9
  27. 594
  28. 18
  29. 264
  30. 6
  31. 161
  32. 51
  33. 18
  34. 16
  35. 228
  36. 165
  37. 18
  38. 6
  39. 24
  40. 17

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