[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 300
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Предлагаю сделать замену переменных: вместо восьмиклассников использовать первокурсниц, а вместо семиклассников - одиннадцатиклассниц.
Then it should be freshmen and eleventh graders. Otherwise the meaning of the substitution is unclear.
Тогда уж первокурсниКи и одиннадцатикласницы. Иначе непонятен смысл замены.
Well, we all have our own views on beauty.Also, the terms do not yet define the ratio of blondes to brunettes
Let's offer them this scheme. The tallest freshman and the tallest eleventh-grader hold hands and walk out of the hall. What they do there is unimportant, but then they come back and stand in front of each other apart from everyone else (with it being quite obvious that the boy is knowingly taller than the girl, as he is taller than the one she was standing with). The ones they left (unless, of course, the tallest ones were standing with each other before) are joined into a new pair. Since in this pair the freshman is taller than the departed highest eleventh-grader (according to the problem, he was standing next to her), he is also taller than the "new" friend. Repeating the iteration we get a ranked row of freshmen enriched with the same number of eleventh-graders, and the ratio "boy is taller than girl" is satisfied in every pair.
Arrange the pairs 7kl - 8kl in ascending order of 7kl from left to right.
In order for an 8kl to be rearranged in ascending order, any 8kl would have to be lower than a 7kl, the original 7kl in front of it would have to be lower than the 7kl on the left, which is impossible because they are ordered.
yeah... you've written, you don't understand.
matinducation
Alsu, it's solved.
Now the second part of the problem is for tenth grade:
75 b) A regiment of soldiers is lined up in a rectangle, so that in each column the soldiers stand by their height.
Prove that if you rearrange them by their height in each column, they will still stand by their height in each column.
Apparently bad in a) the schoolchildren were, since b) the soldiers =)
and c) will there be a cube of aliens?
The tallest soldiers take up their pens and leave the parade ground. What they do there doesn't matter...
The planes belong to the other one, ignore them.
Is this one for eighth graders unfamiliar with linear algebra too?
P.S. If you had to find a set of points P, then the problem would be more interesting.