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3 votes

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^...
Misha Lavrov's user avatar
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5 votes

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
Daniel S's user avatar
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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 ...
Sneftel's user avatar
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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 ...
Gareth McCaughan's user avatar
1 vote

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: ...
Daniel Mathias's user avatar
1 vote

Counting puzzle #1: Function combinations

Computer Assisted Solution: Answer: Algorithm:
Chris Cudmore's user avatar

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