I***e
发帖数: 1136 | 1 You have a pentagon. (5 vertices). On each of them there is a real number. The
sum of all the numbers is positive.
Call the following an "Update": for a negative number, reverse its sign, and
substract the absolute value from each of the two adjacent points (e.g., if
you have 3, -1, 2, then after the "Update" you'll have 2, 1, 1). Note that an
"Update" preserves sum of these numbers.
Prove that no matter what you choose the process will end with finite steps
with all vertices having positive num | m****n
发帖数: 45 | 2 what if 4 of them are positive and the other one is 0?
how do you update?
The
an
【在 I***e 的大作中提到】
: You have a pentagon. (5 vertices). On each of them there is a real number. The
: sum of all the numbers is positive.
: Call the following an "Update": for a negative number, reverse its sign, and
: substract the absolute value from each of the two adjacent points (e.g., if
: you have 3, -1, 2, then after the "Update" you'll have 2, 1, 1). Note that an
: "Update" preserves sum of these numbers.
: Prove that no matter what you choose the process will end with finite steps
: with all vertices having positive num
| I***e
发帖数: 1136 | 3 In this case you can get 4, 1, -2, -1, -1, and so on...
Regarding median's question, the conclusion should be that the in the end all
numbers are non-negative. Sorry for the typo.
-iCare- |
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