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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 128 · 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.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) 126 (b) 45 (c) 42 (d) 14
  2. 2.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 315 (c) 306 (d) 282
  3. 3.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) 57 (b) 171 (c) 60 (d) 19
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  5. 5.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) 30 (b) 9 (c) 27 (d) 81
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 20 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 2 (d) 4
  11. 11.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) 48 (b) 51 (c) 16 (d) 144
  12. 12.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) 337 (c) 327 (d) 336
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  15. 15.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 508 (c) 410 (d) 507
  16. 16.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) 7 (c) 24 (d) 63
  17. 17.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 49 (c) 50 (d) 40
  18. 18.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) 75 (b) 72 (c) 24 (d) 216
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 17 (d) 5
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 16 (c) 17 (d) 15
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 18 (b) 19 (c) 20 (d) 9
  25. 25.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) 27 (b) 72 (c) 24 (d) 8
  26. 26.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 579 (c) 588 (d) 464
  27. 27.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 84 (d) 74
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 6 (b) 4 (c) 7 (d) 5
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  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) 135 (b) 45 (c) 15 (d) 48
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 7 (b) 5 (c) 6 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 4 (c) 16 (d) 14
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 18 (d) 17
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 3 (c) 15 (d) 13
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 4 (d) 2
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 18 (d) 20
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 6 (b) 12 (c) 10 (d) 13

Answer key

  1. 42
  2. 315
  3. 57
  4. 2
  5. 27
  6. 2
  7. 17
  8. 19
  9. 8
  10. 3
  11. 48
  12. 336
  13. 4
  14. 6
  15. 507
  16. 21
  17. 49
  18. 72
  19. 16
  20. 16
  21. 9
  22. 4
  23. 3
  24. 19
  25. 24
  26. 588
  27. 83
  28. 6
  29. 18
  30. 4
  31. 45
  32. 6
  33. 5
  34. 15
  35. 7
  36. 18
  37. 14
  38. 4
  39. 19
  40. 12

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