← Range ArcadeWORLD Nº 012 · THE TOWNS ARE ARITHMETIC
⌂ ruler roadNEXT HALL, EIGHT THOUSAND STEPS, NO LOOKING

TWELVE QUESTIONS. A ROAD THAT IS NEVER BUILT.

Name the town
before you get there.

Settlements stand where the ruler says. The road knows where every one is
without walking. Can you?

THE SURVEYQUESTION 1 / 12
⌂

Every town stands
on a round-number milestone.

Huts stand every 16 steps, cottages every 128, farmsteads every 1,024, halls every 8,192.
Four kinds of question, three of each. The road strip shows what stands nearby, and the answer is always in the pattern.

0 POINTS1 2 3 4 OR CLICK AN ANSWERTHE LONG ROAD

next = ceil((g+1)/2^k)·2^k − 1. census = ⌊(end+1)/2^k⌋ − ⌊start/2^k⌋. biggest = two XORs.

ANOTHER STRETCH OF ROAD

Words choose where along the road the survey begins.

THE SURVEYOR'S NOTES

Four questions the ruler answers instantly.

A settlement of rank k stands at every milestone g with 2^k dividing g+1: huts at k=4, cottages 7, farmsteads 10, halls 13.

Next: how far to the next one of a kind. Census: how many stand in a stretch. Biggest: which milestone in a stretch carries the largest town. Distance: how far to the nearest, forward or back.

Ten points a right answer, a little more on a streak. After you answer, the note shows the one-line formula the road used. Three stars is twelve for twelve.

THE SURVEY IS COMPLETE

⌂

You can see
the towns from here.

A LITTLE ROAD FOR A FRIEND

Walk this road with me.