The 159 constraint is the most common form of “Column Indexer” constraint.
In each row, the digit in column 1 indicates the column in which the digit 1 appears. For example, if column 1 contains a 4, then column 4 is 1. If column 1 is 7, then column 7 is 1.
A corollary is that if column 1 indicates where digit 1 appears, then the column in which digit 1 appears indicates what is in column 1. For example, if column 4 contains a 1, then column 1 is 4. If column 7 is 1, then column 1 is 7.
The same is true for every digit in columns 5 and 9.
Some puzzles tagged with 159 may include additional indexed columns, or indexed rows.
I almost called this one 159 Sandwiches, because my creativity had run out for the day. Then I thought, wait, that’s a ridiculous number of sandwiches. So I changed the name, because really, 159 would be a ridiculous number of sandwiches. Either far too many, or one too few.
But 159 combined with Sandwich Sums, well, that’s a different story entirely.
I see your 159, and raise you 3 and 7. My hand is strong, so I’m willing to keep raising if I have to.
This one also had some testing contoversy, with difficulty estimates and solve times ranging widely.
N is for Number, like the numbers 1, 5, and 9.
N is for Nine, which along with 1 and 5, are indexed columns.
N is for Not planning to continue with this “N is for” routine.