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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 209 · 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) 2 (b) 3 (c) 1 (d) 10
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 6 (b) 5 (c) 7 (d) 8
  3. 3.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) 42 (c) 45 (d) 126
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 2 (d) 1
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  7. 7.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) 216 (b) 75 (c) 24 (d) 72
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 17 (d) 16
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 14 (c) 16 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  13. 13.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) 57 (b) 54 (c) 162 (d) 18
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 20 (d) 19
  16. 16.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) 45 (b) 18 (c) 15 (d) 5
  17. 17.The numbers 19 to 27 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) 69 (c) 23 (d) 207
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 5 (b) 4 (c) 3 (d) 6
  19. 19.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 573 (c) 582 (d) 460
  20. 20.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 438 (d) 429
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 16 (d) 15
  22. 22.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 192 (c) 183 (d) 184
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 8 (b) 17 (c) 19 (d) 18
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 4 (d) 14
  25. 25.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
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 14 (b) 3 (c) 13 (d) 15
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 16 (d) 6
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  34. 34.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) 51 (c) 16 (d) 48
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 1 (d) 2
  36. 36.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) 18 (c) 21 (d) 54
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 18 (d) 20
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  39. 39.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 390 (c) 332 (d) 381
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2

Answer key

  1. 2
  2. 7
  3. 42
  4. 3
  5. 9
  6. 8
  7. 72
  8. 5
  9. 6
  10. 17
  11. 15
  12. 3
  13. 54
  14. 4
  15. 19
  16. 15
  17. 69
  18. 5
  19. 582
  20. 438
  21. 16
  22. 183
  23. 18
  24. 15
  25. 33
  26. 2
  27. 14
  28. 3
  29. 17
  30. 19
  31. 7
  32. 8
  33. 19
  34. 48
  35. 3
  36. 18
  37. 19
  38. 5
  39. 390
  40. 3

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