← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 298 · 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) 72 (c) 8 (d) 27
  2. 2.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) 33 (b) 90 (c) 30 (d) 10
  3. 3.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) 144 (c) 48 (d) 16
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 19 (d) 9
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 8 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  7. 7.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) 39 (b) 42 (c) 117 (d) 13
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  9. 9.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 309 (c) 318 (d) 284
  10. 10.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 516 (c) 526 (d) 525
  11. 11.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) 69 (c) 207 (d) 23
  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) 17 (b) 54 (c) 51 (d) 153
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 4 (c) 16 (d) 14
  14. 14.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 429 (c) 420 (d) 430
  15. 15.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) 69 (c) 198 (d) 66
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 16 (c) 14 (d) 15
  17. 17.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) 5 (c) 45 (d) 15
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 16 (d) 14
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 17 (d) 16
  25. 25.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 543 (c) 544 (d) 434
  26. 26.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 172 (c) 154 (d) 163
  27. 27.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 34 (c) 44 (d) 52
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 3 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  30. 30.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) 21 (d) 7
  31. 31.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 5 (d) 4
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 17 (d) 16
  34. 34.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 528 (c) 538 (d) 537
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  36. 36.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) 135 (c) 15 (d) 45
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  38. 38.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 250 (c) 267 (d) 258
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 21
  40. 40.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 549 (c) 550 (d) 540

Answer key

  1. 24
  2. 30
  3. 48
  4. 19
  5. 19
  6. 8
  7. 39
  8. 4
  9. 318
  10. 525
  11. 69
  12. 51
  13. 15
  14. 429
  15. 66
  16. 15
  17. 15
  18. 6
  19. 5
  20. 15
  21. 7
  22. 3
  23. 3
  24. 17
  25. 543
  26. 163
  27. 43
  28. 4
  29. 9
  30. 21
  31. 42
  32. 4
  33. 16
  34. 537
  35. 20
  36. 45
  37. 2
  38. 267
  39. 20
  40. 549

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