← Range ArcadeWORLD Nº 015 · TAKE THE ROOT, FLIP THE MASK, AGAIN
√ root cellarWHICH DOOR GOES DEEPEST?

FOUR DOORS. ONE MASK. HOW FAR DOWN?

Square roots
all the way down.

Take the root, XOR the mask, take the root again.
Members of the family survive a round or more. Some go deep. Pick the deepest.

THE CELLARROUND 1 / 6 · MASK 5
√

Every door is a member
of the same family.

Each number is (i² XOR m)², so every one survives at least one round.
Choose the door whose descent lasts longest.
A span that is a perfect square hides a secret room.

0 POINTS1 2 3 4 OR CLICK A DOORDOWN WE GO

441 → 21 → 16 → 4 → 1 → 1 → 4 → 2 → 7, and it only stops because 7 is not a square.

ANOTHER SET OF DOORS

Words choose which members stand behind the doors.

THE CELLAR MAP

One round is a root and a flip.

Start with a number. If it is a perfect square, take its root and XOR the mask; that is one round. Keep going until the number stops being square.

Every door shows a member of the family (i² XOR m)², so every door survives the first round. Some members stand on top of others and go several rounds deep. Pick the deepest. Ties count.

Ten points plus the depth for a right pick. If the chosen door's span to its neighbour is itself a square, that is a Pythagorean triple and a fifteen-point secret room. Masks change every round. Three stars is six for six.

THE CELLAR IS MAPPED

√

You know
which way is down.

A LITTLE CELLAR FOR A FRIEND

Come down the cellar with me.