New answers tagged combinatorics
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I am not giving a new solution. But I'd like to propose a nicer expression of the solution given for the general case $n=2^k$.
In fact my solution is the same as noedne's.
And the explanation why it works is the same as OHO's.
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Having a Blokus Trigon set at hand was a big help!
I arrived at a different actually the same solution as pointed out:
My approach was rather straightforward, here's how I went around it:
Hint 1:
Hint 2:
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Started by scaling the goal, I put one-by-one with some trial-and-error in the end to find this solution:
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I asked a question over on Math.SE, pointing to this puzzle, and @Elaqqad gave a very long answer with lots of links to math that might help. @Elaqqad also produced a concrete solution with only 59 tests — beating @noedne's long-standing solution of 63 tests!
Background math
The "wolves and sheep" puzzle is a specific case of non-adaptive group testing. ...
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It is possible for the $3\times3$ square:
Here is an explanation of how I found those solutions:
For $11\times11$:
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Previous answer, valid before alteration to question.
The maximum area is
if one
Note that
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The medians have values ranging from 2 to 8, so exactly one of these values does not appear as the median of one of the 6 rows/columns.
Here are three templates that allow you to choose any missing median value.
For completeness, here are the solutions this produces:
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No 2:
No 3:
No 4:
No 5:
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Here is one solution:
0
I'm 3 years late to this puzzle, but I think I just solved it in 29 steps, and I'm too gosh darned proud to not post my answer. Especially since I struggled to follow some of the other answers.
For the sake of my work, I label the balls as W1-W15, with the W1 being the lightest and W15 being the heaviest.
Sorts 1-5:
There are a few very important facts ...
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Starting off short before the end of this answer we take
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From JS1's answer we already see that this is impossible for normal dice. But assuming the dice's result are dependent on each other as if they could communicate,
This is how it works:
Let's pick a "nice" solution:
Actual numbers:
2
6
Here is one way to do it
General Strategy
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Here is one solution:
I solved it by
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It is
Because
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It can be:
If:
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You can't make it in a fair way, as JS1 answered.
But given lateral thinking tag - you could have dice where one influences the other. Perhaps by magic or magnets. For example, first die is fair (1/6 chance of any number) and when it rolls 1, there is 6/11 chance of rolling 1 on the second one and 1/11 to roll any other number. Symmetry tells us 6 should ...
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I think:
Here's my proof:
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We can test this statement by the following:
However I doubt this is the "lateral thinking" the OP has in mind.
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