For Countdown (a British quiz show), is there any way we can prove a numbers game is impossible?
Proving that a numbers puzzle on Countdown is impossible
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number-theory
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0Exhaustive search - there are only a finite number of options, so the full set of possible calculations can be enumerated. Beyond that, though, this problem is likely to be formally hard - it's a very close cousin to things like subset-sum problems that are known to be NP-complete. This means that a truly 'efficient' algorithm for the problem is highly unlikely. – 2017-01-21
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0Ah, I was wondering if something like this link could be done for it. https://www.youtube.com/watch?v=AZR2ND4l_5Y – 2017-01-21
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1Not in any succinct form - that question is innately 'one-dimensional' in a way, because we're evaluating a polynomial in one variable; the Countdown question is innately multi-dimensional, because _all_ of the numbers are available as arguments. – 2017-01-21