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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 583 · 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.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 433 (c) 360 (d) 423
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 5 (b) 3 (c) 2 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  6. 6.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) 75 (c) 216 (d) 72
  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) 42 (b) 24 (c) 34 (d) 33
  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) 32 (b) 22 (c) 31 (d) 40
  9. 9.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) 63 (c) 60 (d) 20
  10. 10.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) 42 (b) 126 (c) 45 (d) 14
  11. 11.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) 5 (b) 18 (c) 45 (d) 15
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 2 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 14 (d) 15
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 16 (d) 17
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 18 (d) 17
  17. 17.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 185 (c) 176 (d) 194
  18. 18.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 387 (c) 330 (d) 388
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  20. 20.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 362 (c) 436 (d) 426
  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) 54 (b) 17 (c) 51 (d) 153
  22. 22.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) 66 (b) 22 (c) 198 (d) 69
  23. 23.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) 6 (b) 54 (c) 18 (d) 21
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 5 (d) 6
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
  26. 26.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) 42 (b) 13 (c) 39 (d) 117
  27. 27.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 81 (d) 72
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 16 (c) 14 (d) 15
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 17 (d) 18
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 5 (b) 4 (c) 7 (d) 6
  31. 31.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) 15 (b) 48 (c) 135 (d) 45
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  34. 34.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) 90 (b) 10 (c) 33 (d) 30
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 17
  36. 36.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 378 (c) 450 (d) 459
  37. 37.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
  38. 38.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 332 (d) 391
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
  40. 40.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 361 (c) 312 (d) 360

Answer key

  1. 432
  2. 6
  3. 9
  4. 4
  5. 8
  6. 72
  7. 33
  8. 31
  9. 60
  10. 42
  11. 15
  12. 3
  13. 4
  14. 14
  15. 16
  16. 18
  17. 185
  18. 387
  19. 4
  20. 435
  21. 51
  22. 66
  23. 18
  24. 6
  25. 4
  26. 39
  27. 81
  28. 15
  29. 18
  30. 6
  31. 45
  32. 8
  33. 3
  34. 30
  35. 18
  36. 459
  37. 48
  38. 390
  39. 16
  40. 360

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