← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 121 · 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 two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  3. 3.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 322 (c) 321 (d) 286
  4. 4.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 114 (c) 104 (d) 113
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  6. 6.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 174 (c) 173 (d) 164
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 6 (d) 5
  8. 8.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 195 (c) 205 (d) 208
  9. 9.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 321 (c) 292 (d) 331
  10. 10.The numbers 14 to 22 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) 162 (c) 18 (d) 57
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  12. 12.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) 66 (b) 21 (c) 63 (d) 189
  13. 13.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) 10 (c) 33 (d) 30
  14. 14.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) 22 (b) 66 (c) 69 (d) 198
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 3 (d) 5
  16. 16.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 166 (c) 176 (d) 175
  17. 17.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 328 (c) 385 (d) 384
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 3 (b) 4 (c) 1 (d) 2
  19. 19.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) 16 (c) 48 (d) 51
  20. 20.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) 36 (b) 11 (c) 99 (d) 33
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  23. 23.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 459 (d) 378
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 15 (c) 5 (d) 16
  25. 25.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) 23 (b) 207 (c) 69 (d) 72
  26. 26.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 470 (c) 597 (d) 598
  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) 153 (b) 51 (c) 54 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  29. 29.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 92 (c) 102 (d) 110
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 5 (b) 16 (c) 15 (d) 17
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 19 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  33. 33.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 498 (c) 640 (d) 630
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 16 (b) 18 (c) 9 (d) 19
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 7 (b) 6 (c) 8 (d) 5
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  37. 37.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 399 (c) 344 (d) 409
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 11 (c) 13 (d) 14
  39. 39.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 547 (c) 436 (d) 546
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11

Answer key

  1. 4
  2. 2
  3. 321
  4. 113
  5. 6
  6. 173
  7. 5
  8. 204
  9. 330
  10. 54
  11. 9
  12. 63
  13. 30
  14. 66
  15. 4
  16. 175
  17. 384
  18. 3
  19. 48
  20. 33
  21. 3
  22. 3
  23. 459
  24. 15
  25. 69
  26. 597
  27. 51
  28. 4
  29. 101
  30. 16
  31. 19
  32. 8
  33. 639
  34. 18
  35. 7
  36. 4
  37. 408
  38. 13
  39. 546
  40. 9

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