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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 887 · 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 times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 8 (d) 20
  2. 2.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) 54 (c) 162 (d) 57
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 5 (b) 2 (c) 3 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  5. 5.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) 48 (d) 51
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 5 (d) 4
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  9. 9.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 484 (c) 394 (d) 483
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 16 (b) 15 (c) 17 (d) 5
  12. 12.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) 9 (b) 30 (c) 27 (d) 81
  13. 13.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 171 (d) 57
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 16 (b) 17 (c) 15 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  16. 16.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 436 (c) 546 (d) 537
  17. 17.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
  18. 18.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) 279 (c) 288 (d) 289
  19. 19.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) 189 (b) 66 (c) 21 (d) 63
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 17 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  27. 27.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 525 (d) 535
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 12 (c) 10 (d) 11
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 15 (c) 14 (d) 3
  30. 30.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) 39 (c) 13 (d) 117
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  32. 32.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 471 (c) 481 (d) 392
  33. 33.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) 45 (d) 135
  34. 34.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 143 (d) 134
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (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) 15 (b) 18 (c) 45 (d) 5
  37. 37.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 108 (c) 99 (d) 90
  38. 38.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 18 (d) 17
  40. 40.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 630 (c) 639 (d) 640

Answer key

  1. 19
  2. 54
  3. 4
  4. 9
  5. 48
  6. 7
  7. 4
  8. 20
  9. 483
  10. 6
  11. 16
  12. 27
  13. 57
  14. 16
  15. 5
  16. 546
  17. 66
  18. 288
  19. 63
  20. 16
  21. 18
  22. 4
  23. 6
  24. 8
  25. 16
  26. 9
  27. 534
  28. 11
  29. 14
  30. 39
  31. 4
  32. 480
  33. 45
  34. 143
  35. 17
  36. 15
  37. 99
  38. 3
  39. 18
  40. 639

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