last byte

I M A G E B Y A N D R I J B O R Y S A S S O C I A T E S

to one kilometer in the first turn, the second player then takes up to two kilometers, the first player then gets up to three kilometers, the second then gets up to four kilometers, and so on.

 

Warm-up. Suppose the line segment is five kilometers long from a stake at kilometer 0 to a stake at kilometer 5. Suppose the first player takes between 0 and 1 kilometer. Which player would get more of the line segment, assuming each plays optimally?

Answer to warm-up. Player 2. Player
1 takes kilometer 0 to 1. Player 2 then
takes kilometers 2 to 4. The first play-
er then takes one of the two remain-
ing kilometers— 1 to 2 or 4 to 5—and
the second player then takes the oth-
er remaining kilometer. The second
player ends up with lease rights to
three of the
protocol, whereby each company
(player) takes turns to acquire non-
overlapping sections of a full seg-
ment. The first player may take up

THE VAST UNDERGROUND lava fields in the western U.S. feature a photogenic geyser called Old Faithful. Eruptions send approximately 15,000 liters of steaming water 50 meters into the air approximately every hour. Unfortunately, what is underground is not nearly as appealing. If the lava fields erupted in a major way, they could cause ferocious firestorms that would destroy a large portion of the western U.S. and Canada and substantially cool the planet.

Now imagine a pair of tunnel-boring energy-extraction companies are competing to cool the lava, make some money, and provide carbon-free energy besides. The idea is to tunnel from a power plant outside the lava fields to near the lava, but not too close, to avoid accidental eruptions. A pipeline could in theory then take cool water from the power plant to the end of the tunnel where the water would be heated into steam and the steam would power the turbines of the power plant. The whole system could be designed to recycle the steam back into water in a closed loop.

In this scenario, the federal government, which owns the land, steps in to lease the energy rights, identifying cross-sections underground to which tunnels can be drilled. The government identifies those underground cross-sections based on their more-or-less linear segments aboveground, so leasing a segment would confer the right to tap the lava in the vertical cross-section below that segment.

To encourage participation in the project while achieving equity for both companies, government mathematicians design a game-style Upstart Puzzles

Fighting for Lava

[CONTINUED ON P. 143]

DOI: 10.1145/3314071 Dennis Shasha

Imagine a pair
of tunnel-boring
energy-extraction
companies are
competing to cool
the lava, make some
money, and provide
carbon-free
energy besides.

“First player gets to claim up to
one kilometer, the second up to two, the
first up to three, and so on. Should I try to go
first or second in order to maximize
my access to the lava fields.”