← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 534 · 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 15? (a) 5 (b) 16 (c) 3 (d) 4
  2. 2.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 88 (d) 97
  3. 3.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 516 (d) 517
  4. 4.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 288 (c) 289 (d) 279
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 9 (c) 7 (d) 8
  6. 6.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 398 (c) 480 (d) 490
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 4 (d) 1
  8. 8.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 40 (c) 31 (d) 32
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  10. 10.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) 21 (b) 24 (c) 63 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  14. 14.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 321 (c) 204 (d) 213
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  17. 17.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 541 (d) 531
  18. 18.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) 51 (c) 54 (d) 153
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  21. 21.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 58 (d) 68
  22. 22.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 49 (c) 40 (d) 58
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 17 (d) 16
  24. 24.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 276 (c) 286 (d) 262
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 13 (b) 15 (c) 14 (d) 3
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 9 (d) 21
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 18 (d) 17
  28. 28.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 436 (c) 426 (d) 435
  29. 29.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) 162 (b) 57 (c) 54 (d) 18
  30. 30.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) 45 (c) 126 (d) 42
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 13 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  34. 34.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 222 (c) 220 (d) 223
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 10 (c) 9 (d) 6
  36. 36.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) 5 (d) 45
  37. 37.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) 72 (b) 8 (c) 27 (d) 24
  38. 38.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 324 (c) 217 (d) 207
  39. 39.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 196 (c) 187 (d) 188
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 18 (d) 16

Answer key

  1. 4
  2. 97
  3. 516
  4. 288
  5. 8
  6. 489
  7. 3
  8. 31
  9. 8
  10. 21
  11. 3
  12. 6
  13. 2
  14. 213
  15. 4
  16. 2
  17. 540
  18. 51
  19. 5
  20. 4
  21. 67
  22. 49
  23. 17
  24. 285
  25. 14
  26. 20
  27. 17
  28. 435
  29. 54
  30. 42
  31. 14
  32. 5
  33. 9
  34. 222
  35. 9
  36. 15
  37. 24
  38. 216
  39. 187
  40. 17

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