← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 639 · 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 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) 24 (b) 8 (c) 72 (d) 27
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  3. 3.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 411 (c) 402 (d) 346
  4. 4.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 60 (d) 50
  5. 5.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) 7 (c) 24 (d) 21
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 18 (d) 19
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 4 (c) 14 (d) 16
  8. 8.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 254 (c) 274 (d) 273
  9. 9.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) 490 (c) 480 (d) 489
  10. 10.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 57 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 20 (d) 8
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 16
  14. 14.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 36 (c) 39 (d) 108
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  16. 16.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) 21 (c) 18 (d) 6
  17. 17.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 217 (c) 207 (d) 216
  18. 18.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) 48 (b) 45 (c) 15 (d) 135
  19. 19.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 268 (c) 267 (d) 258
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 6 (d) 16
  21. 21.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) 17 (c) 54 (d) 51
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  23. 23.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 543 (d) 534
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 5 (b) 2 (c) 3 (d) 4
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 5 (d) 3
  27. 27.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) 18 (b) 54 (c) 162 (d) 57
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 6 (b) 9 (c) 8 (d) 7
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 7 (c) 5 (d) 4
  30. 30.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 145 (c) 136 (d) 146
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  33. 33.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 597 (c) 588 (d) 598
  34. 34.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) 9 (b) 30 (c) 81 (d) 27
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 19 (d) 18
  36. 36.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 78 (c) 60 (d) 69
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 5 (d) 4
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 7 (c) 17 (d) 18
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 8 (b) 7 (c) 9 (d) 10
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 16 (d) 18

Answer key

  1. 24
  2. 4
  3. 411
  4. 59
  5. 21
  6. 18
  7. 15
  8. 273
  9. 489
  10. 57
  11. 6
  12. 19
  13. 15
  14. 36
  15. 8
  16. 18
  17. 216
  18. 45
  19. 267
  20. 17
  21. 51
  22. 5
  23. 543
  24. 2
  25. 4
  26. 4
  27. 54
  28. 8
  29. 6
  30. 145
  31. 2
  32. 8
  33. 597
  34. 27
  35. 19
  36. 69
  37. 6
  38. 18
  39. 9
  40. 17

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