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The Centrifuge Problem
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A centrifuge has n
identical slots, each big enough to fit one test tube. To prevent this centrifuge from wobbling, k
identical tubes must be placed into these slots so that their mutual center of gravity lies precisely at the center of the centrifuge. This problem was inspired by yet another video “The Centrifuge Problem”, which you may watch below. Alternatively, whose eyes read faster than their ears listen can check out Matt Baker’s post “The Balanced Centrifuge Problem”.
So, balancing k
test tubes into n
slots turns out to be possible if and only if both k, n-k
can be expressed as sums of prime factors of n
, repetition of factors allowed. For example, when n
equals 6 whose prime factors are 2 and 3, the centrifuge can hold 0, 2, 3, 4 (= 2 + 2) or 6 (= 3 + 3) test tubes.
However, there is no possible way to balance 1 or 5 test tubes in six slots. Even though 5 = 2 + 3 satisfies the first part of the rule, there is no way to counterbalance the remaining empty slot, which is required despite the counterintuitive fact that empty slots weigh nothing!
This function does not actually need to construct the balanced configuration of k
test tubes, but merely determine whether at least one balanced configuration exists for the given n, k
.
Input: Two integers (int)
Output: Logic value (bool).
Examples:
assert balanced_centrifuge(6, 3) == True assert balanced_centrifuge(7, 0) == True assert balanced_centrifuge(15, 8) == False
CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.
In order to install CheckiO client you'll need installed Python (version at least 3.8)
Install CheckiO Client first:
pip3 install checkio_client
Configure your tool
checkio --domain=py config --key=
Sync solutions into your local folder
checkio sync
(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)
checkio serv -d
Alternatevly, you can install Chrome extension or FF addon
checkio install-plugin
checkio install-plugin --ff
checkio install-plugin --chromium
Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.
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