6
votes
If there are 6 men and 6 women around a table, what's the probability that both groups are joined in a single cluster each?
There are $12!$ possible seating patterns, and $6!\cdot6!$ patterns of people for each pattern of gender, so $\dfrac{12!}{6!\cdot6!}=\dbinom{12}6=924$ gender patterns. There are 12 rotations of the ...
- 2,946
5
votes
Accepted
Longest subsequences and shortest longest ones
A best possible sequence is
which has a longest increasing subsequence of length 3 and a longest decreasing of length...
Another example is
which has
These are best possible because
- 5,793
4
votes
Accepted
Nimber Mnemonics
Multiplication of nimbers between $1$ and $15$ (or between $0$ and $2^{2^n}-1$ for any $n$) has a primitive root: a number whose powers generate all the nimbers we want. (In fact, I believe that $2^{2^...
- 1,779
3
votes
Accepted
Nimber mnemonic combinatorial puzzle
There are 384 solutions. Here's one:
I used integer linear programming as follows. Let $$P=\{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o\}$$ be the set of positions, where position $o$ must take ...
- 12k
3
votes
Counting puzzle #1: Function combinations
Computerless solution
There are
in the set S.
Let's first of all consider
Well, actually
Anyway, we aren't done yet, because
We now have
Now we need to augment our list by
We're still not quite ...
- 117k
1
vote
Accepted
Counting puzzle #1: Function combinations
Programmed solution:
These numbers are listed below, along with the function that produces them.
C code to identify and count the numbers:
...
- 13.4k
1
vote
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