four-questions is one function. Everything below was drawn by it when the site was
last published, at settings taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and when the generator changes, this
page changes with it.
With nothing specified
Four questions, one strip The same crease pattern asked four different things. Deciding stops at the first answer, counting cannot stop at all, listing pays for the answer as well as the search, and asking whether a machine can make it is a question about sequences rather than about states — a different search over a different space. 6 creases, 7 segments, assignment MVMVMV Does it fold flat? at most 5,040 orderings, and it may stop early yes as far as the first legal one How many ways? every one of them, because the last is as likely as the first 1 5,040 orderings What are they? the same search, paying a second time for what it keeps 1 stackings, written out 5,040 orderings, and the answer as well Can a machine make it? a different search, over sequences of folds rather than over stackings yes 1,350 states the four are not four difficulties of one problem — they are four problems the cost is work rather than time — a clock reading would differ on every build
assignment: "MVMVMV"Four questions, one strip The same crease pattern asked four different things. Deciding stops at the first answer, counting cannot stop at all, listing pays for the answer as well as the search, and asking whether a machine can make it is a question about sequences rather than about states — a different search over a different space. 6 creases, 7 segments, assignment MVMVMV Does it fold flat? at most 5,040 orderings, and it may stop early yes as far as the first legal one How many ways? every one of them, because the last is as likely as the first 1 5,040 orderings What are they? the same search, paying a second time for what it keeps 1 stackings, written out 5,040 orderings, and the answer as well Can a machine make it? a different search, over sequences of folds rather than over stackings yes 1,350 states the four are not four difficulties of one problem — they are four problems the cost is work rather than time — a clock reading would differ on every build
creases: [0.14, 0.28, 0.42, 0.57, 0.71, 0.85], assignment: "MVMVMV"Four questions, one strip The same crease pattern asked four different things. Deciding stops at the first answer, counting cannot stop at all, listing pays for the answer as well as the search, and asking whether a machine can make it is a question about sequences rather than about states — a different search over a different space. 6 creases, 7 segments, assignment MVMVMV Does it fold flat? at most 5,040 orderings, and it may stop early yes as far as the first legal one How many ways? every one of them, because the last is as likely as the first 1 5,040 orderings What are they? the same search, paying a second time for what it keeps 1 stackings, written out 5,040 orderings, and the answer as well Can a machine make it? a different search, over sequences of folds rather than over stackings no 1,275 states the four are not four difficulties of one problem — they are four problems the cost is work rather than time — a clock reading would differ on every build
creases: [0.125, 0.25, 0.375, 0.5, 0.625, 0.75], assignment: "MVMVMV"Four questions, one strip The same crease pattern asked four different things. Deciding stops at the first answer, counting cannot stop at all, listing pays for the answer as well as the search, and asking whether a machine can make it is a question about sequences rather than about states — a different search over a different space. 6 creases, 7 segments, assignment MVMVMV Does it fold flat? at most 5,040 orderings, and it may stop early yes as far as the first legal one How many ways? every one of them, because the last is as likely as the first 1 5,040 orderings What are they? the same search, paying a second time for what it keeps 1 stackings, written out 5,040 orderings, and the answer as well Can a machine make it? a different search, over sequences of folds rather than over stackings yes 414 states the four are not four difficulties of one problem — they are four problems the cost is work rather than time — a clock reading would differ on every build
What it checked while it drew
Collected while it drew, not written by hand.
The count is how many separate times that claim was put to the test.
the assignment has one letter per crease, so the four questions are asked about one object ×1
Where it is called
Every figure listed here is drawn by the same rule, so a mistake in the rule would be in all
of them at once, and so would a correction.
A no costs more than a yes
When a folding question comes back yes, it comes back with an object: a labelling, a stacking, a folded state that anybody can check in one pass. When it comes back no, it comes back with nothing but the assurance that a search looked everywhere — and that assurance is the first thing to break.
Four questions about one sheet
Deciding, counting, listing and optimising are not four difficulties of one problem. They are four problems, and folding is the subject that proves it: a ruled map is trivial to decide and unsolved to count, while a general crease pattern is the other way round.
What a checker cannot check
Every crease pattern on this site is run past four theorems before it is allowed onto a page, and passing all four proves nothing. The gap is not a bug to be closed: it is the NP-hardness result, arriving as a property of a hundred lines of code.
All the figures ·
The what it costs to know field ·
The patterns a reader can fold