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# Fire Island

[P5 Maths and Up: Rate]

Have I got a puzzle for you this fortnight.

One of the most famous riddles of the old-world was, understandably, a high-stakes challenge: if the riddle was answered wrongly, you would be eaten alive.

"What walks on four legs in the morning, two legs in the afternoon and three legs in the evening?" so declared the Sphinx to all who tried entering Thebes. Oedipus replied, "Man: as an infant, he crawls on all fours; as an adult, he walks on two legs and; in old age, he uses a walking stick." His reward for beating the Sphinx was witnessing it plummeting into the ocean in shock, gaining entry into Thebes, the accidental murder of his father, marrying his mother and stabbing his own eyes out upon realising what he had done. Maybe he should have answered the Sphinx wrongly, and saved everyone the trouble of chronicling his biography, and reading it as well.

Some level of jeopardy makes puzzles a lot more exciting. While I don't exactly qualify as a sphinx, allow me to present to you an equally tricky puzzle to wrestle your way out of.

*** FIRE ISLAND ***

You are stranded on a rectangular plot of land that stretches 400m from North to South, and 3km from West to East. The land is surrounded by high cliffs, which means the only escape possible is by waiting for a helicopter to arrive; even the physically fit wouldn't dare to scale a cliff edge prone to breaking off and killing them in one drop. Within the plot of land is a forest that has not experienced rainfall for a long time, rendering it combustible. Due to the layout of the land being next to a sea, a constant breeze blows from west to east. At the far west of the island is an abandoned lightning rod, surrounded by a patch of dried trees. Need a visual to help you?

So, yeah. Lots of combustible trees, surrounded by cliffs, some vague idea that the sea is somewhere near you. There's too much going on to mention the dimensions, but that's 400m for its breadth and 3km for its length.

So. On Tuesday, a storm passed, it hit the lightning rod & the entire western strip is on fire. It'll keep climbing eastward at a rate of 100m/hr and burn you alive at the rate it's going. If you're trapped by the fire, or if you attempt to scale the cliff under these conditions where the hot air makes your palms too sweaty to get a good grip on the cliff sides, you will die with a probability of 1, which is to say 'certain death'.

Well. Not all hope is lost, you have a backpack! And within the backpack are four items: A compass, a calculator, a pen knife and a copy of GLM Economics. To make things happier for you, a rescue helicopter is bound for your position in about... 66 hours. So you need to survive against the fire (or miraculously put it out) somehow. (please don't try to put it out, you'll die trapped by flames faster than you can put it out)

How do you survive until Thursday?