Kotze
26th March 2012, 22:45
Imagine a planned economy introducing a new standard "week" containing as many working days as free days for you, the proposals:
6-day sequence: 1 day work, 1 day off, 2 days work, 2 days off, repeat.
8-day sequence: 2 days work, 1 day off, 2 days work, 3 days off, repeat.
12-day sequence: 2 days work, 2 days off, 4 days work, 4 days off, repeat.
16-day sequence: 4 days work, 2 days off, 4 days work, 6 days off, repeat.
With such a sequence it's possible to have people in groups that differ in when the sequence starts/ends, so capacity load of factories and transportation is balanced over the days, and still everybody shares free days with everyone else, like this (each column shows a day, each horizontal line a group, x = work, o = no work):
6-day sequence: 6 groups, you are guaranteed to share at least 1 free day within 6 days with any other working person. When a person is randomly drawn from the working population, the chance that person has at least 2 free days in common with you is 1/3.
xoxxoo
oxoxxo
ooxoxx
xooxox
xxooxo
oxxoox
8-day sequence: 4 groups, you are guaranteed to share at least 1 free day within 8 days with any other working person. When a person is randomly drawn from the working population, the chance that person has at least 2 free days in common with you is 1/2.
xxoxxooo
xoooxxox
oxxoooxx
ooxxoxxo
12-day sequence: 6 groups, you are guaranteed to share at least 2 free consecutive days within 12 days with any other working person. When a person is randomly drawn from the working population, the chance that person has at least 4 free days in common with you, in no more than 2 segments, is 1/3.
xxooxxxxoooo
ooxxooxxxxoo
ooooxxooxxxx
xxooooxxooxx
xxxxooooxxoo
ooxxxxooooxx
16-day sequence: 4 groups, you are guaranteed to share at least 2 free consecutive days within 16 days with any other working person. When a working person is randomly drawn from the population, the chance that person has at least 4 free days in common with you, in no more than 2 segments, is 1/2.
xxxxooxxxxoooooo
xxooooooxxxxooxx
ooxxxxooooooxxxx
ooooxxxxooxxxxoo
6-day sequence: 1 day work, 1 day off, 2 days work, 2 days off, repeat.
8-day sequence: 2 days work, 1 day off, 2 days work, 3 days off, repeat.
12-day sequence: 2 days work, 2 days off, 4 days work, 4 days off, repeat.
16-day sequence: 4 days work, 2 days off, 4 days work, 6 days off, repeat.
With such a sequence it's possible to have people in groups that differ in when the sequence starts/ends, so capacity load of factories and transportation is balanced over the days, and still everybody shares free days with everyone else, like this (each column shows a day, each horizontal line a group, x = work, o = no work):
6-day sequence: 6 groups, you are guaranteed to share at least 1 free day within 6 days with any other working person. When a person is randomly drawn from the working population, the chance that person has at least 2 free days in common with you is 1/3.
xoxxoo
oxoxxo
ooxoxx
xooxox
xxooxo
oxxoox
8-day sequence: 4 groups, you are guaranteed to share at least 1 free day within 8 days with any other working person. When a person is randomly drawn from the working population, the chance that person has at least 2 free days in common with you is 1/2.
xxoxxooo
xoooxxox
oxxoooxx
ooxxoxxo
12-day sequence: 6 groups, you are guaranteed to share at least 2 free consecutive days within 12 days with any other working person. When a person is randomly drawn from the working population, the chance that person has at least 4 free days in common with you, in no more than 2 segments, is 1/3.
xxooxxxxoooo
ooxxooxxxxoo
ooooxxooxxxx
xxooooxxooxx
xxxxooooxxoo
ooxxxxooooxx
16-day sequence: 4 groups, you are guaranteed to share at least 2 free consecutive days within 16 days with any other working person. When a working person is randomly drawn from the population, the chance that person has at least 4 free days in common with you, in no more than 2 segments, is 1/2.
xxxxooxxxxoooooo
xxooooooxxxxooxx
ooxxxxooooooxxxx
ooooxxxxooxxxxoo