← Range ArcadeWORLD Nº 019 · SORT BY THE LOW BITS
📮 milestone postEVERY PARCEL KNOWS ITS CART

TEN WAVES. FIVE CARTS. ONE RULE.

The address
is the arithmetic.

A parcel for milestone 8,191 goes on the hall cart, because 8,192 is 2¹³.
Read the low bits of g+1 and the cart is obvious.

THE SORTING ROOMWAVE 0 / 10
📮

Huts at 2⁴, cottages 2⁷,
farmsteads 2¹⁰, halls 2¹³.

Each parcel shows its milestone and, on easy shifts, the binary of g+1.
Drag the cart token onto the parcel. Nothing standing there? Return to sender.

$0 · SERVED 0DRAG AN ITEM ONTO A CUSTOMER · TAP A DISH TO COOKSECOND CLASS

rankOf(g) is v2(g+1) against the ranks 4, 7, 10, 13: a count of trailing zeros, no lookup.

ANOTHER SACK OF PARCELS

Words choose which milestones come down the belt.

SORTING NOTES

Count the trailing zeros.

A settlement of rank k stands at milestone g when 2^k divides g+1: huts at k=4, cottages 7, farmsteads 10, halls 13. So a parcel's cart is the number of trailing zero bits of g+1, and fewer than four means nobody lives there: return to sender.

Drag a cart token onto the parcel. A wrong cart costs the parcel patience and comes back to you. Easy shifts print the binary on the label; harder shifts do not.

Each sorted parcel pays by its rank. Three parcels falling off the belt in one wave closes the room; ten waves, or a hundred dollars, wins.

THE SHIFT IS OVER

📮

Every order,
every wave.

A LITTLE SORTING ROOM FOR A FRIEND

Sort the post with me.