[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 339
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Конечно, задача сильно усложняется и становится интереснее, если есть требование, чтобы решения были целыми. Хотя и здесь видна закономерность: положительные имеют вид 4к+1, 4к+2, 4к+3, 4к+4.
Yes with whole numbers the problem gets interesting.
Here are some more answers.
-1 3 5 24 46 -16560
-1 3 5 26 40 -15600
-1 3 5 28 36 -15120
-1 3 5 31 32 -14880
....
Can anyone find ALL the solutions ?
Может кто то может найти ВСЕ решения ?
I think this can only be possible if all solutions suddenly group into similar series.
Which in themselves are infinite, but can be described by "generators" as functions of natural k.
-1 3 5 26 40 -15600
-1 3 5 28 36 -15120
-1 3 5 31 32 -148802 avatara: I'm not going to contrast this thread with euroflood. Let it be exactly what it is - a more or less closed circle of interest.
Can the second player play in such a way that any move by the first player results in a palindrome (i.e. a word that reads the same from left to right and from right to left)?
To be continued. Such a greedy bastard...
The answer is yes. The permutations must be made with an odd number of letters and starting with the third, so that each permutation respects the palindrome
Ответ - да. Перестановки нужно совершать при нечетном количестве букв и начиная с третей, так чтобы при каждой перестановке соблюдался палиндром
It doesn't work that way.
Let's say it was
ABABA or BAAAB.
add BB first
ABABA + BB
BAAAB + AA → no
BAAAB + BB
BBAAABB + AA → no
BABABAB +BB
BBBAAABB +AA → no
The thought process is as follows:
1)A+AB=ABA=ABA.
2)AV+AV=AVAVAV=AVAVAV
3) ABHABAB+AB=ABABHAB=ABHABEA (the third A is moved to the end of the word)
4)AVHABABAB+AB=ABHABAB=ABHABABAB (move the first letter to the middle).
etc.
But it doesn't say swap the nearby (those in close proximity) two.
Но ведь не сказано что менять местами близлежайшие (те что в непосредственной близости) две.
in close proximity - not necessarily
but how to get a palindrome
BBAAABB + AA