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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 714 · 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 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 187 (c) 188 (d) 196
  2. 2.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 45 (d) 36
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 15 (d) 16
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 11 (b) 7 (c) 8 (d) 10
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 9 (d) 10
  6. 6.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) 153 (b) 54 (c) 51 (d) 17
  7. 7.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) 69 (c) 72 (d) 207
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 18 (d) 16
  9. 9.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) 21 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 21 (c) 9 (d) 19
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 18 (d) 17
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 3 (d) 6
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 6 (d) 5
  17. 17.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) 81 (b) 9 (c) 30 (d) 27
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 20
  19. 19.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) 39 (b) 12 (c) 36 (d) 108
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 18
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 9 (b) 13 (c) 11 (d) 14
  22. 22.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) 21 (c) 66 (d) 63
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  27. 27.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) 48 (c) 144 (d) 16
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  29. 29.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 396 (c) 387 (d) 336
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 9 (d) 10
  31. 31.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  32. 32.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) 126 (d) 45
  33. 33.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) 8 (b) 27 (c) 24 (d) 72
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 10 (b) 11 (c) 3 (d) 9
  35. 35.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 106 (c) 114 (d) 105
  36. 36.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 101 (d) 92
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  38. 38.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) 72 (b) 75 (c) 216 (d) 24
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 11 (c) 6 (d) 9
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 17 (d) 16

Answer key

  1. 187
  2. 45
  3. 16
  4. 10
  5. 9
  6. 51
  7. 69
  8. 17
  9. 18
  10. 6
  11. 2
  12. 20
  13. 8
  14. 18
  15. 5
  16. 5
  17. 27
  18. 19
  19. 36
  20. 17
  21. 13
  22. 63
  23. 2
  24. 4
  25. 4
  26. 5
  27. 48
  28. 9
  29. 396
  30. 9
  31. 3
  32. 42
  33. 24
  34. 10
  35. 105
  36. 101
  37. 17
  38. 72
  39. 11
  40. 17

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