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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 432 · 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 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 19 (d) 20
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 7 (b) 6 (c) 9 (d) 8
  4. 4.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) 72 (c) 75 (d) 24
  5. 5.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 282 (d) 291
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 15 (b) 16 (c) 17 (d) 5
  7. 7.How many times is the digit 7 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 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 2 (d) 4
  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) 21 (b) 18 (c) 54 (d) 6
  10. 10.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) 16 (b) 51 (c) 144 (d) 48
  11. 11.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) 81 (c) 27 (d) 9
  12. 12.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
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 16 (c) 15 (d) 13
  14. 14.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) 162 (c) 18 (d) 54
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  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) 7 (b) 63 (c) 21 (d) 24
  17. 17.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) 5 (b) 15 (c) 45 (d) 18
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 17 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  22. 22.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) 207 (b) 69 (c) 23 (d) 72
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  24. 24.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 258 (c) 259 (d) 249
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 4 (d) 5
  26. 26.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) 10 (c) 33 (d) 30
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 4 (d) 2
  28. 28.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 7 (c) 9 (d) 8
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 3 (d) 4
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 2 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  33. 33.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 369 (c) 318 (d) 360
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 1 (d) 4
  35. 35.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) 135 (d) 45
  36. 36.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  37. 37.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) 51 (c) 153 (d) 17
  38. 38.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) 250 (c) 240 (d) 249
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 3 (d) 6

Answer key

  1. 19
  2. 7
  3. 8
  4. 72
  5. 291
  6. 16
  7. 4
  8. 4
  9. 18
  10. 48
  11. 27
  12. 57
  13. 15
  14. 54
  15. 19
  16. 21
  17. 15
  18. 17
  19. 6
  20. 5
  21. 7
  22. 69
  23. 3
  24. 258
  25. 4
  26. 30
  27. 3
  28. 177
  29. 8
  30. 5
  31. 3
  32. 4
  33. 369
  34. 3
  35. 45
  36. 2
  37. 51
  38. 249
  39. 2
  40. 5

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