Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 194
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Another problem:
Is it possible to place three white kings and five black queens on a 5x5 board so that white is not under check?
The weight is 4.
I'll post a couple more in the evening.
As a practitioner, I ask, what is the fastest way to get a result?
What problem are you talking about? If you mean weighing - see above.
If it is about any, the general recipe is this: you have to look for and clarify the constraints (impossibilities). Then what remains is a solution; if nothing remains, there is guaranteed to be no solution.
Or as an aphorism: "The fool looks at the possibilities, the wise man looks at the limitations." (ц)
I would write: GENIALLY, if the problem were solved manually )
What problem are you referring to? If about weighing - see above.
If it is about any, the general recipe is this: you have to look for and clarify the constraints (impossibilities). Then what remains is the solution, if nothing remains, the solution is guaranteed to be non-existent.
Or as an aphorism: "A fool looks at the possibilities, a wise man looks at the limitations. (ц)
Even manually such problems are solved by brute force, and this is not genius.
There is a mathematical explanation for any combination, if you think about it you wouldn't have to do it manually, unfortunately I don't have these explanations, as opposed to the scientific method of groping.
SZZ: such problems are offered at math olympiads, do you think that they will waste time on searches?
I'm talking about balls, and exactly the way to solve the problem in practice that will take the least time to arrange the balls, if it takes 0.1 second to count one ball, and 1 second to weigh a pile.
It is when you work with a specific counting/weighing machine, then this approach (taking time into account) will make sense.
I would have written: GENIAL if the task had been solved manually )
So the problem was solved manually. A crossword puzzle with large squares was used as a matrix. And then I did it quickly - I have MS Office 2013, as it were.
I've seen a problem somewhere about 8 queens standing on a board and not disturbing each other, I was able to place five queens and 8 queens not.)
It is when you work with a specific counting/weighing machine that this approach (in terms of time) will make sense.