← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 78 · 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 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 50 (d) 32
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  3. 3.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 70 (c) 88 (d) 80
  4. 4.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) 69 (b) 198 (c) 22 (d) 66
  5. 5.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 168 (d) 158
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  7. 7.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) 72 (c) 75 (d) 216
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 8 (c) 7 (d) 5
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 8 (b) 17 (c) 19 (d) 18
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 14 (d) 3
  14. 14.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
  15. 15.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) 465 (c) 475 (d) 474
  16. 16.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
  17. 17.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 422 (c) 525 (d) 526
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  19. 19.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 92 (c) 74 (d) 83
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 2 (d) 4
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 20 (d) 8
  22. 22.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) 63 (b) 66 (c) 21 (d) 189
  23. 23.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) 30 (b) 27 (c) 9 (d) 81
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 18 (d) 16
  25. 25.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 411 (c) 412 (d) 346
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 18 (d) 17
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 15 (d) 16
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 6 (b) 9 (c) 7 (d) 8
  30. 30.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 364 (d) 439
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 1 (d) 4
  32. 32.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 393 (c) 384 (d) 334
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 4 (d) 6
  36. 36.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) 10 (b) 30 (c) 33 (d) 90
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 18 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  39. 39.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
  40. 40.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) 63 (c) 60 (d) 20

Answer key

  1. 41
  2. 2
  3. 79
  4. 66
  5. 167
  6. 6
  7. 72
  8. 9
  9. 4
  10. 7
  11. 18
  12. 3
  13. 14
  14. 48
  15. 474
  16. 21
  17. 525
  18. 6
  19. 83
  20. 4
  21. 19
  22. 63
  23. 27
  24. 17
  25. 411
  26. 3
  27. 17
  28. 15
  29. 8
  30. 438
  31. 3
  32. 393
  33. 5
  34. 20
  35. 5
  36. 30
  37. 19
  38. 2
  39. 51
  40. 60

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