← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 189 · 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 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 4 (d) 3
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 5 (b) 6 (c) 8 (d) 7
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 21 (c) 9 (d) 19
  4. 4.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) 81 (b) 9 (c) 27 (d) 30
  5. 5.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 248 (c) 255 (d) 264
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 17
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 11 (b) 14 (c) 8 (d) 13
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 5 (c) 4 (d) 2
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  10. 10.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) 21 (b) 6 (c) 54 (d) 18
  11. 11.The numbers 1 to 9 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) 5 (c) 15 (d) 45
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  14. 14.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 7 (c) 24 (d) 63
  15. 15.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 290 (c) 327 (d) 318
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  17. 17.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 334 (d) 333
  18. 18.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 342 (c) 352 (d) 351
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 3 (d) 2
  20. 20.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 144 (c) 154 (d) 162
  21. 21.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 132 (d) 114
  22. 22.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 181 (c) 190 (d) 182
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  24. 24.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) 135 (b) 48 (c) 15 (d) 45
  25. 25.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 213 (c) 204 (d) 321
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 4 (d) 15
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 17 (c) 6 (d) 18
  28. 28.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 151 (c) 142 (d) 160
  29. 29.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 615 (c) 624 (d) 625
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  31. 31.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 136 (c) 118 (d) 127
  32. 32.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 474 (c) 465 (d) 475
  33. 33.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 440 (d) 552
  34. 34.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) 144 (d) 16
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 2 (b) 5 (c) 3 (d) 4
  36. 36.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 336 (c) 397 (d) 396
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 13 (c) 4 (d) 14
  38. 38.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 198 (c) 189 (d) 190
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  40. 40.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 66 (c) 63 (d) 21

Answer key

  1. 4
  2. 7
  3. 20
  4. 27
  5. 264
  6. 18
  7. 13
  8. 4
  9. 2
  10. 18
  11. 15
  12. 4
  13. 3
  14. 21
  15. 327
  16. 3
  17. 333
  18. 351
  19. 3
  20. 153
  21. 123
  22. 181
  23. 3
  24. 45
  25. 213
  26. 15
  27. 17
  28. 151
  29. 624
  30. 6
  31. 127
  32. 474
  33. 552
  34. 48
  35. 4
  36. 396
  37. 13
  38. 189
  39. 19
  40. 63

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