← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 857 · 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 2? (a) 10 (b) 2 (c) 1 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  3. 3.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 331 (c) 292 (d) 330
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  5. 5.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 327 (c) 337 (d) 336
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 7 (d) 17
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 6 (d) 4
  8. 8.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) 48 (c) 51 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19
  12. 12.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 360 (c) 351 (d) 361
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
  14. 14.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) 15 (b) 18 (c) 5 (d) 45
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 17 (d) 18
  16. 16.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) 108 (b) 36 (c) 12 (d) 39
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  18. 18.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 369 (c) 379 (d) 378
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  20. 20.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) 153 (d) 54
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 5 (b) 6 (c) 3 (d) 4
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 17 (d) 16
  23. 23.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 336 (d) 387
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  25. 25.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) 420 (c) 429 (d) 430
  26. 26.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) 45 (b) 14 (c) 42 (d) 126
  27. 27.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 220 (c) 210 (d) 218
  28. 28.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
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 2 (d) 5
  30. 30.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 274 (c) 303 (d) 304
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 7 (d) 17
  32. 32.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 633 (c) 642 (d) 500
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 4 (d) 7
  34. 34.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) 33 (c) 36 (d) 99
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 4 (d) 15
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 2 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  39. 39.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
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 4 (d) 3

Answer key

  1. 2
  2. 9
  3. 330
  4. 9
  5. 336
  6. 18
  7. 5
  8. 48
  9. 5
  10. 8
  11. 19
  12. 360
  13. 18
  14. 15
  15. 17
  16. 36
  17. 7
  18. 378
  19. 4
  20. 51
  21. 5
  22. 16
  23. 396
  24. 3
  25. 429
  26. 42
  27. 219
  28. 97
  29. 4
  30. 303
  31. 17
  32. 642
  33. 6
  34. 33
  35. 3
  36. 15
  37. 4
  38. 5
  39. 21
  40. 5

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