combinatorics

  1. Order of alternating-sign-matrix function

  2. Problem about Pictures
  3. How many different patterns to transport load with these condition?

  4. Relaxed Menage Problem - sitting arrangement for couples

  5. How does $\dbinom{n}{k}\dbinom{n}{n - k}$ differ from $\dbinom{n}{k}$?
  6. Construction Of Minimal Set With Sum Property
  7. Figuring out all possible combinations for a given circumstance

  8. Zeta polynomial of the Boolean Lattice

  9. Calculating all possible combinations in string of letters/digits (they can repeat) if for example "B" and "8" aren't allowed to be next to each other

  10. Combinatoric: How many binary strings of length 4 have exact two zeroes?

  11. On the size of intersection of subsets

  12. Sum of rolls greater than the product
  13. Rolling 5 dice, probability of a double.

  14. Points and lines in an infinite projective plane

  15. Calculate $\sum\limits_{k=0}^{20}(-1)^k\binom{k+2}2$ without calculating each term separately

  16. 6 periods and 5 subjects
  17. What good algorithms are there for shuffling (scrambling) 1 to n objects?

  18. Time to first success for a simple event

  19. Maximum volume of a parallelepiped

  20. Sum and product of 3 integer random variables

  21. Random draw from bins

  22. Inclusion/Exclusion Counting

  23. What is expectation value of times to pick items out from the box which number of picked out items is random integer in each time?

  24. Rooks on a Chessboard
  25. Arrange the integers $1,2,\dots,n$ in a row such that the number of times that an integer is bigger than the previous integer is $m$.

  26. Exam with 12 yes/no questions (half yes, half no) and 8 correct needed to pass, is it better to answer randomly or answer exactly 6 times yes?

  27. show that the maximum of $xy+ xz + yz$ is when $x = y = z$

  28. Choosing 4 cards randomly from a standard deck of 52 cards, what is the probability the 4 cards add up to 20? (Without Replacement)
  29. inclusion-exclusion: class distribution so that professor teaches the same two courses both semesters
  30. Birthday problem: using $^nC_r$.
  31. 100 Prison Problem- Why does this solution not work?
  32. Number of triple of sequences
  33. Distribute $30$ marks to $8$ problems

  34. Finding the minimum cardinal value of intersection of 4 sets.

  35. 2 player throw darts alternately. Find the probability generating function and expected number of throws

  36. Say "red" with playing cards

  37. Why is this result using binomial coefficients true?

  38. number of ways putting m nonadjacent balls in a n*n*n chess board

  39. Union of each family of a list of subsets and of specific length, equaling to the original set?

  40. Card Game Probability 13 Card Hand

  41. inclusion-exclusion problem - sitting arrangement
  42. Stacking math books

  43. Inviting four people to dinner if one of them can be invited only if that person's two friends will be there as well

  44. knights and knaves... and a traveller

  45. Optimal strategy for guessing subset of given size
  46. How was this formula arrived?

  47. Is there any formula for the following permutation?

  48. Arrangements of 3 baskets, 2 misses through Combinations or Permutations?

  49. Finding out two unknown constants of a division
  50. Prove the set partition identity via double counting argument

  51. Recurrence relation problem — the forbidden sequences

  52. $N$ series of $n$ independent trials, and Time to first success for equiprobable events

  53. Can this product be written as a summation?

  54. Number of ways to connect sets of $k$ dots in a perfect $n$-gon
  55. Probability that all three dice show different numbers exactly two times when rolled three times simultaneously
  56. How many $6$-digit numbers contain each of the digits $1$, $2$, and $3$ at least once?
  57. Probability questions in involving combinatorics

  58. creating a Free-For-All (1v1v1v1) schedule for 20 teams over 13 weeks
  59. Characterizing multisets that are the sum of two permutations
  60. Convergence of $\sum_{m=0}^{n-1}\frac{1}{(n+2)!}\left|\sum_{k=0}^{m+1}(-1)^k\binom{n+3}{k}(m+2-k)^{n+1}\right|$ as $n\rightarrow\infty$
  61. Can every partial transversal be extended to a maximum partial transversal?

  62. Time to first success in case of increasing probability at each trial
  63. Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
  64. Distributing $3$ identical prizes to $10$ players

  65. How many combinations are possible in a $4 \times 4$ grid?

  66. Graph with exactly K bridges
  67. How many "marvelous" points inside a triangle.

  68. Differentiating cases in counting problems

  69. Need help to understand some combination of six digits

  70. Beads on a Bracelet

  71. How many 6-digit numbers can I write?

  72. How many even integers are between 20000 and 70000 in which no digit is repeated?

  73. Number of triplets of collinear points in a standard setting
  74. Really Complicated Combinatorics

  75. Stirling Numbers of the Second Kind $ \sum_{j= m}^n {j \brace m} (m+1)^{n-j} = {n+1\brace m+1} $

  76. How many sequences with a maximum of four signs of the Morse alphabet can be formed?

  77. How many even integers between $100$ and $1000$ have distinct digits?

  78. How many different words can be made?
  79. The Number Of Integer Solutions Of Equations

  80. threshold graph and degree sequence proof

  81. How many diagonals in a decagon?

  82. Not a strictly mathematical question, but complex one nonetheless
  83. Stirling Numbers $ \sum_{j= m}^{n-r} \binom{n}j {j \brace m} {n-j\brace r} = \binom{m} {m+r} {n\brace m+r} $ Combinatorical Proof or Algebraic

  84. Summation of this series.

  85. Towers 'n Tets problem.
  86. How many shared numbers between all factors of 465 and all multiples of 3 between 20 and 100?

  87. Casework on Cards

  88. Random Walk (Combinatorics: number of ways to reach end of the straight line)
  89. Coin Toss Experiment Problem
  90. Combinatorics in real life problems
  91. Tight Acute Sets
  92. Circular Permutation, clockwise and counterclockwise can't be distinguished?

  93. What is the algorithm to generate the cards in the game "Dobble" ( known as "Spot it" in the USA )?h

  94. Problem about clubs

  95. Proving $|A+B| \geq |A|+|B| - 1$ for $A,B \subseteq \mathbb{Z}$ finite and non-empty

  96. Why not count automorphisms when counting - total number of spanning trees in $K_5$

  97. How to prove the maximum number of chords those can not across more than one other chord from points around the circle?

  98. How many number of classes over matrices with $\pm 1$ entries are there, where equivalence means row/column permutation and multiplication?
  99. Garden with mushrooms

  100. Question about solving combinatorics.