← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 772 · 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 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) 6 (b) 54 (c) 18 (d) 21
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  3. 3.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) 36 (c) 11 (d) 99
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  5. 5.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) 72 (b) 23 (c) 69 (d) 207
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  7. 7.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) 15 (c) 45 (d) 5
  8. 8.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 141 (c) 150 (d) 132
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  11. 11.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 54 (c) 45 (d) 46
  12. 12.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) 595 (c) 468 (d) 594
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 5 (d) 15
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 5 (d) 3
  20. 20.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 494 (c) 633 (d) 624
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 2 (d) 5
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 5 (b) 7 (c) 6 (d) 4
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 14 (c) 5 (d) 15
  25. 25.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) 72 (b) 75 (c) 24 (d) 216
  26. 26.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) 16 (b) 51 (c) 48 (d) 144
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
  29. 29.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
  30. 30.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 628 (c) 627 (d) 618
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 18 (d) 19
  33. 33.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 373 (c) 320 (d) 372
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 19 (d) 8
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 6 (b) 15 (c) 14 (d) 16
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 3 (b) 2 (c) 5 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 21 (d) 20
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 7 (c) 10 (d) 5
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5

Answer key

  1. 18
  2. 5
  3. 33
  4. 8
  5. 69
  6. 18
  7. 15
  8. 141
  9. 2
  10. 19
  11. 45
  12. 594
  13. 15
  14. 9
  15. 7
  16. 6
  17. 7
  18. 3
  19. 4
  20. 633
  21. 8
  22. 4
  23. 6
  24. 15
  25. 72
  26. 48
  27. 6
  28. 18
  29. 30
  30. 627
  31. 2
  32. 18
  33. 372
  34. 19
  35. 15
  36. 4
  37. 3
  38. 20
  39. 9
  40. 4

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