← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 175 · 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.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  2. 2.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 414 (d) 348
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  4. 4.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) 57 (c) 162 (d) 54
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 6 (d) 18
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 3 (c) 14 (d) 13
  7. 7.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 24 (c) 33 (d) 42
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  9. 9.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) 144 (b) 16 (c) 51 (d) 48
  10. 10.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) 11 (b) 99 (c) 33 (d) 36
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 3 (d) 4
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 15 (b) 5 (c) 16 (d) 14
  13. 13.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 129 (d) 120
  14. 14.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 535 (b) 525 (c) 428 (d) 534
  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) 198 (b) 22 (c) 69 (d) 66
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 14 (d) 15
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 14 (c) 3 (d) 13
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 16 (d) 17
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 2
  23. 23.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) 402 (c) 411 (d) 346
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 6 (c) 5 (d) 7
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  26. 26.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
  27. 27.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 402 (c) 496 (d) 495
  28. 28.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  30. 30.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) 66 (b) 63 (c) 189 (d) 21
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 7 (b) 4 (c) 5 (d) 6
  32. 32.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 553 (d) 552
  33. 33.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) 537 (d) 538
  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) 81 (b) 9 (c) 30 (d) 27
  35. 35.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) 20 (c) 60 (d) 63
  36. 36.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 266 (d) 292
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  38. 38.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) 42 (c) 45 (d) 126
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  40. 40.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 319 (c) 309 (d) 284

Answer key

  1. 5
  2. 414
  3. 3
  4. 54
  5. 17
  6. 14
  7. 33
  8. 9
  9. 48
  10. 33
  11. 5
  12. 15
  13. 129
  14. 534
  15. 66
  16. 15
  17. 14
  18. 4
  19. 2
  20. 4
  21. 16
  22. 4
  23. 411
  24. 6
  25. 18
  26. 72
  27. 495
  28. 5
  29. 6
  30. 63
  31. 6
  32. 552
  33. 537
  34. 27
  35. 60
  36. 291
  37. 8
  38. 42
  39. 19
  40. 318

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