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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 616 · 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 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) 18 (b) 54 (c) 6 (d) 21
  2. 2.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) 15 (c) 18 (d) 5
  3. 3.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 240 (c) 249 (d) 250
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 14 (b) 15 (c) 5 (d) 16
  5. 5.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) 19 (c) 171 (d) 60
  6. 6.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 76 (d) 66
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 6 (b) 8 (c) 5 (d) 7
  8. 8.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) 33 (c) 30 (d) 10
  9. 9.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) 23 (b) 72 (c) 207 (d) 69
  10. 10.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 291 (c) 272 (d) 300
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 8 (b) 5 (c) 10 (d) 11
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 17 (d) 16
  15. 15.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 113 (c) 104 (d) 114
  16. 16.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) 8 (c) 72 (d) 24
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 4 (d) 3
  18. 18.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 471 (c) 462 (d) 472
  19. 19.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 22 (c) 32 (d) 31
  20. 20.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 41 (c) 42 (d) 32
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 4 (b) 5 (c) 2 (d) 3
  22. 22.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
  23. 23.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 54 (c) 63 (d) 72
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 8 (d) 18
  25. 25.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) 20 (b) 180 (c) 63 (d) 60
  26. 26.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 289 (c) 288 (d) 264
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  28. 28.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) 21 (b) 66 (c) 189 (d) 63
  29. 29.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) 24 (b) 7 (c) 21 (d) 63
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 20 (c) 19 (d) 8
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 18 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 9 (c) 16 (d) 19
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 5 (c) 4 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  36. 36.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) 45 (c) 126 (d) 42
  37. 37.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) 117 (b) 13 (c) 42 (d) 39
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 9 (b) 8 (c) 10 (d) 7
  39. 39.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) 12 (b) 108 (c) 39 (d) 36
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

  1. 18
  2. 15
  3. 249
  4. 15
  5. 57
  6. 75
  7. 7
  8. 30
  9. 69
  10. 300
  11. 20
  12. 9
  13. 10
  14. 16
  15. 113
  16. 24
  17. 4
  18. 471
  19. 31
  20. 41
  21. 4
  22. 51
  23. 63
  24. 19
  25. 60
  26. 288
  27. 3
  28. 63
  29. 21
  30. 19
  31. 19
  32. 4
  33. 18
  34. 6
  35. 2
  36. 42
  37. 39
  38. 9
  39. 36
  40. 4

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