Pure maths, physics, chemistry, etc.: brain-training tasks that have nothing to do with trade [Part 2] - page 5

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OK. Let it be your coding.

I've come up with a solution. I'll have a smoke and think about how to word it more precisely.

 
MetaDriver: But there's something to it, maybe you just need to swap the wand for a stochastic... :))
Or the waving to WMA (weighted). But I don't really believe it.
 

So there we have it:

a) A sequence of four cards can encode a number from 0 to 23.

b) always have the possibility of setting aside one card to create one of the three cases:

. . 1. the internal range (between 2 and 3 of the declared cards) is greater than the external range (from 0 to the first declared + from the fourth declared to 51), while the internal range is less than 23

. . 2. the outer range is greater than the inner range, while the outer range is less than 23

. . 3. The above ranges are equal, with each being less than 23 .

Then the coding is as follows: the sequence is coded in cases 1 and 2 as the smallest of the two ranges, in case 3 as any of the two, but pre-agreed between trickster and helper. (e.g. for clarity, external).

// Without prejudice to the solution, willing to relax the strict "less" to <=23

:)

--

Seems to be without holes now.

Please ask for a counterexample.

 
MetaDriver:

So we have:

Even the conditions are overdone. In the case of 1 and 2, it is necessary and sufficient that the smallest of the two ranges (external or internal) is less than or equal to 24.

This way the feasibility of the condition is much more obvious.

 

Let me see, that's a tricky one.

Four Aces + King of clubs. Inside - no more than 6 (51-45 max), outside - at least king minus 0, i.e. >=45.

1. not fulfilled, because inner is less than outer.

2. outer - yes, bigger than inner, but outer is bigger than 23

3. they are not equal.

 
Mathemat:
Let me see, it's complicated.

I was wondering the same thing. It seems that in the simplified version conflicts are possible. Then let's go back to the first one.

--

But the solution's in here somewhere.

 
Mathemat:

Let me see, that's a tricky one.

Four Aces + King of clubs. Inside is no bigger than 1, outside is at least king minus 0, i.e. >=45.

1. not fulfilled, because inside is less than outside.

2. outer - yes, greater than inner, but outer is greater than 23

3. they are not equal.

No, simplification rules. For the first formulation you have already found a counterexample, it is no good. For the second, I don't see any collision yet.
 
So, your rule again: if the ranges are not equal, encode the smallest one. If they are equal, say the outer one. Right?
 
So the smallest of the two ranges is taken (encoded). I don't see any collisions. Four cards cover (remove from range) at least five numbers, so there is always a definite solution.
 
Mathemat:
So, your rule again: if the ranges are not equal, encode the smallest one. If they are equal, say the outer one. Right?
Yeah. And equality always seems to be avoided altogether.
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