I thought I understood this description of the puzzles:
"Each cage shows a result and an operation (+ - × or :)
The operation applied to the numbers in the cage should produce the result shown.
Note that for subtraction and division the order is not fixed (!)"
I found this description to be a bit difficult to follow, so I was using this instead:
For a cage of size N with a “-“ operation and a result R, any set of N numbers is acceptable so long as it can be partitioned into two non-empty subsets where the sum of one subset is R greater than the sum of the other subset.
Then I encountered a puzzle where a 3-block cage had "1-" but my solution of {3,2,2} was not allowed.
According to my interpretation, it should have been allowed since 2+2-3==1.
So, please clarify what the meaning of "-" is in cages of size >2.
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Another explanation I sometimes use for subtraction & division:
there exists an ordering of the numbers in the cage for which the target result is achieved.
there exists an ordering of the numbers in the cage for which the target result is achieved.
OK, good. The biggest number minus all the other ones gives the value shown.
That is much clearer than the posted definition. Thanks.
And that makes the puzzles much easier to reason about because my definition involves many more possible partitions of the set. Nice.
That is much clearer than the posted definition. Thanks.
And that makes the puzzles much easier to reason about because my definition involves many more possible partitions of the set. Nice.
Now, about the ratio ":" operator...
Can it ever apply to cages of size other than 2?
Can it ever apply to cages of size other than 2?
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Yes, and that really is a consequence of me limiting the clue to >= 0.
(I thought that clues like "-2-" would confuse people even more).
The kenken people decided that subtraction/division cages with more than 2 cells
were too complicated, so in those puzzles they are 2 cells only.
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One number minus all the other ones gives the value shown. It's not necessarily the biggest if the puzzle allows for negative numbers.noggin wrote: ↑Mon May 04, 2026 10:40 am OK, good. The biggest number minus all the other ones gives the value shown.
That is much clearer than the posted definition. Thanks.
And that makes the puzzles much easier to reason about because my definition involves many more possible partitions of the set. Nice.
A useful solving strategy is that that number is half the sum of all the numbers in the cage plus the result of the operation (i.e. the value shown)
It's not necessarily the biggest if the puzzle allows for negative numbers.
Good catch.
And I will bracket the following expression to remove an ambiguity:
A useful solving strategy is that there is a number that is
1/2 * (the sum of all the numbers in the cage + the given value)
Good tip.
Good catch.
And I will bracket the following expression to remove an ambiguity:
A useful solving strategy is that there is a number that is
1/2 * (the sum of all the numbers in the cage + the given value)
Good tip.