← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 620 · 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.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 306 (c) 352 (d) 342
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 20 (d) 9
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 6 (b) 5 (c) 7 (d) 8
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  6. 6.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) 18 (c) 6 (d) 21
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  8. 8.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) 42 (c) 13 (d) 39
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  10. 10.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) 24 (b) 216 (c) 75 (d) 72
  11. 11.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 198 (d) 207
  12. 12.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
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  16. 16.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 480 (c) 490 (d) 489
  17. 17.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) 45 (c) 15 (d) 48
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  20. 20.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) 72 (b) 24 (c) 8 (d) 27
  21. 21.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 43 (c) 52 (d) 34
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 8 (c) 9 (d) 6
  23. 23.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 546 (c) 556 (d) 555
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
  25. 25.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 642 (c) 500 (d) 643
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  27. 27.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) 45 (b) 5 (c) 15 (d) 18
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
  31. 31.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) 162 (b) 18 (c) 57 (d) 54
  32. 32.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) 63 (b) 24 (c) 7 (d) 21
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
  36. 36.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 77 (c) 86 (d) 78
  37. 37.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 376 (c) 375 (d) 322
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 5 (b) 6 (c) 4 (d) 3
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 17 (b) 14 (c) 8 (d) 16
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 16 (d) 6

Answer key

  1. 351
  2. 3
  3. 20
  4. 7
  5. 8
  6. 18
  7. 4
  8. 39
  9. 8
  10. 72
  11. 207
  12. 51
  13. 19
  14. 2
  15. 17
  16. 489
  17. 45
  18. 15
  19. 9
  20. 24
  21. 43
  22. 8
  23. 555
  24. 17
  25. 642
  26. 17
  27. 15
  28. 15
  29. 6
  30. 16
  31. 54
  32. 21
  33. 5
  34. 7
  35. 18
  36. 77
  37. 375
  38. 5
  39. 16
  40. 17

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