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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 165 · 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 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 3 (d) 5
  2. 2.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) 27 (c) 9 (d) 30
  3. 3.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 345 (c) 302 (d) 346
  4. 4.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) 6 (c) 21 (d) 54
  5. 5.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) 33 (b) 30 (c) 90 (d) 10
  6. 6.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
  7. 7.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 399 (d) 338
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 16 (c) 17 (d) 18
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 18 (b) 17 (c) 8 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  12. 12.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) 72 (d) 23
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 16 (d) 15
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 17 (d) 16
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 9 (b) 8 (c) 10 (d) 7
  17. 17.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) 42 (b) 45 (c) 14 (d) 126
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 6 (b) 15 (c) 16 (d) 17
  19. 19.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) 18 (b) 15 (c) 45 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  23. 23.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 133 (c) 124 (d) 142
  24. 24.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) 108 (b) 39 (c) 36 (d) 12
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 15 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  27. 27.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 156 (c) 155 (d) 164
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 21
  29. 29.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 96 (d) 95
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 4 (b) 5 (c) 6 (d) 7
  31. 31.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 252 (d) 261
  32. 32.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 393 (c) 384 (d) 394
  33. 33.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) 60 (b) 20 (c) 180 (d) 63
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  36. 36.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 498 (c) 410 (d) 508
  37. 37.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) 72 (d) 24
  38. 38.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) 60 (b) 171 (c) 57 (d) 19
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 15 (c) 4 (d) 14

Answer key

  1. 5
  2. 27
  3. 345
  4. 18
  5. 30
  6. 312
  7. 399
  8. 4
  9. 17
  10. 18
  11. 8
  12. 69
  13. 16
  14. 17
  15. 4
  16. 9
  17. 42
  18. 16
  19. 15
  20. 2
  21. 18
  22. 4
  23. 133
  24. 36
  25. 16
  26. 5
  27. 155
  28. 20
  29. 95
  30. 6
  31. 270
  32. 393
  33. 60
  34. 4
  35. 7
  36. 507
  37. 24
  38. 57
  39. 9
  40. 15

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