POUR
POUR
Level 03 · Units of Two. Both capacities are even, so half of every scale names amounts no pour can produce, and what is left is level one in units of two.
- 01Tap the tap, a vessel, or the drain to say where the water comes from, then tap where it goes.
- 02A six and a ten share a factor of two, so nothing here can ever leave an odd amount standing.
- 03The struck numbers are the amounts no play produces. The rungs are the heights the water can rest at.
POUR, Measure it out. Two vessels, one mark.
Vessels of whole-number capacity, a tap above them and a drain below. Fill one from the tap, empty one into the drain, or pour one into the other until the source runs out or the target fills up, and leave the marked amount standing in a vessel. Underneath it is arithmetic rather than a parity: the tap adds a whole capacity, the drain takes one away, and a pour moves water without changing the total, so whatever is standing in a vessel is a whole-number combination of the capacities. Bezout says that set is exactly the multiples of their greatest common divisor, which means a scale marked in ones can be describing amounts no sequence of pours will ever produce. This is the arcade's first game whose invariant is a subgroup rather than a count, and the ladder is what that costs: at first every mark is reachable and the puzzle is which way round the cycle to go, then the tap goes and the bottom of the scale turns to fiction, and later half of it is a lie.
- 01Tap the tap, a vessel, or the drain to say where the water comes from, then tap where it goes.
- 02A pour stops when the source runs out or the target fills up, whichever happens first.
- 03Leave the marked amount standing in a vessel. Nothing here can strand you, only cost you.
- Level 01 · Two Ways Roundpar 6
A three, a five and a mark at four, and the only two moves the board opens with cost six pours and eight.
- Level 02 · Never Emptypar 7
No tap and no drain, so the twelve units in the big vessel are all the water there is, and the bottom three numbers on its scale are amounts no play can produce.
- Level 03 · Units of Twopar 6
Both capacities are even, so half of every scale names amounts no pour can produce, and what is left is level one in units of two.
controls: Tap where the water comes from, then where it goes
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