Combinatorics

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This is maths as it should be.  Forget about your everyday problems involving random numbers, symbols and so forth scattered everywhere, where the solution involves writing it in tensor notation, summing to infinity, then dividing by zero.  These are problems you can visualise!

Probably the most famous combinatorial problem is the FourColourTheory.

Don't they join together to make Devastator?
Wasn't that the Stunticons? You may be thinking of the Constructicons, who combined to make... let me see... no, you're right, the Constructicons made Devastator.  The Stunticons made Menasor...

PeterTaylor has been wondering recently how many Countdown problems there are given that the 6 numbers are the variables a to f. The best he's been able to do so far is take into account the symmetry of the + and * operators, to get SUM r = 1 to 6 of 3^(r - 1) 6Pr Cr (where 6Pr is 6! / (6 - r)! and Cr is (2r)! / (r! (r + 1)!)). Anyone get a tighter upper bound? The obvious next thing to do is associativity...
On a slightly related note, what proportion of Countdown problems are soluble?  And to move into stats for a moment, what proportion are soluble-by-n, meaning that there is a solution no more than 'n' away from the given number.  --Vitenka

CategoryMaths

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