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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 696 · 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 13? (a) 7 (b) 5 (c) 6 (d) 14
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  3. 3.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 5 (d) 7
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 17 (b) 5 (c) 15 (d) 16
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  8. 8.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) 17 (b) 54 (c) 153 (d) 51
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 6 (d) 4
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  11. 11.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 612 (c) 603 (d) 613
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 10 (b) 13 (c) 8 (d) 12
  13. 13.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) 24 (b) 75 (c) 216 (d) 72
  14. 14.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) 63 (d) 66
  15. 15.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) 19 (b) 60 (c) 57 (d) 171
  16. 16.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 420 (c) 429 (d) 358
  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) 9 (b) 81 (c) 27 (d) 30
  18. 18.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 318 (c) 327 (d) 290
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  21. 21.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 340 (c) 330 (d) 298
  22. 22.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 583 (d) 460
  23. 23.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 535 (b) 534 (c) 428 (d) 525
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 13 (c) 9 (d) 14
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 7 (c) 5 (d) 6
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 2 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  29. 29.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) 126 (c) 45 (d) 14
  30. 30.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 342 (c) 406 (d) 405
  31. 31.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) 63 (b) 180 (c) 20 (d) 60
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 3 (d) 2
  34. 34.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) 24 (c) 27 (d) 72
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 17 (b) 8 (c) 19 (d) 18
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 8 (b) 9 (c) 7 (d) 6
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 3 (d) 2
  38. 38.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) 48 (b) 16 (c) 51 (d) 144
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 9 (c) 5 (d) 6
  40. 40.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 137 (c) 128 (d) 138

Answer key

  1. 6
  2. 9
  3. 225
  4. 7
  5. 16
  6. 5
  7. 2
  8. 51
  9. 6
  10. 4
  11. 612
  12. 12
  13. 72
  14. 63
  15. 57
  16. 429
  17. 27
  18. 327
  19. 7
  20. 5
  21. 339
  22. 582
  23. 534
  24. 13
  25. 6
  26. 4
  27. 4
  28. 7
  29. 42
  30. 405
  31. 60
  32. 6
  33. 3
  34. 24
  35. 18
  36. 8
  37. 4
  38. 48
  39. 8
  40. 137

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