Department numbers: Difference between revisions
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Note that we are only showing the distinct valid [[combinations]] here, not all valid [[permutations]] of those combinations. (Valid permutations would be: swapping the last two values in a combination, and all permutations of 2 4 6.) |
Note that we are only showing the distinct valid [[combinations]] here, not all valid [[permutations]] of those combinations. (Valid permutations would be: swapping the last two values in a combination, and all permutations of 2 4 6.) |
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Another variation would be more constraint based, blindly implementing the rules of the task and yielding all valid permutations: |
Another variation would be more constraint based, blindly implementing the rules of the task and yielding all valid permutations. (Shown here with the number of possibilities at each step): |
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<syntaxhighlight lang=J> NB. 3 departments, 1..7 in each |
<syntaxhighlight lang=J> NB. 3 departments, 1..7 in each |
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rule1=. >,{3#<1+i.7 |
#rule1=. >,{3#<1+i.7 |
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343 |
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NB. total must be 12, numbers must be unique |
NB. total must be 12, numbers must be unique |
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rule2=. (#~ ((3=#@~.) * 12=+/)"1) rule1 |
#rule2=. (#~ ((3=#@~.) * 12=+/)"1) rule1 |
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30 |
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NB. no odd numbers in police department (first department) |
NB. no odd numbers in police department (first department) |
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rule3=. (#~ 0=2|{."1) rule2 |
#rule3=. (#~ 0=2|{."1) rule2 |
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14 |
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rule3 |
rule3 |
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2 3 7 |
2 3 7 |
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