The Doppit Almanac · No. 36

Boxit

Cut the grid into boxes that fit their numbers

What it is

Boxit is Shikaku. Numbers are scattered across the grid, and each one is the size of a box drawn around it. Cut the whole grid into those boxes: rectangles of whole squares, one number to a box, each covering exactly as many squares as its number says. Nothing is left over at the end.

No box may hold two numbers, which rules out more than it first looks. A 6 with another number three squares along cannot run that way, so it goes elsewhere. Most of the solving is that: count the ways a number could sit, cross off the ones covering a second number or running off the edge, and take the one left.

The other half reads it the other way round. Pick an empty square and ask which numbers can still reach it. When only one can, that square belongs to it, and its box usually follows.

How it plays

Cut the whole grid into boxes. Every box is a rectangle of whole squares.
Each box holds one number, and covers exactly that many squares.
Every square ends up in exactly one box.
Tap one corner of a box, then tap the opposite corner. Tap a box you have drawn to take it away.
A box that covers the wrong number of squares turns red.
On Expert some boxes show a question mark instead of their number. A question mark box can be any size, and together those boxes cover the squares the numbers leave over.
Stuck? Hint names the next box with nowhere else to go, then draws it.

The difficulties

Easy is five by five with boxes of two to five squares, about half a minute of counting. Medium is eight by eight, the same work at more of it. Hard is ten by ten, picked for boards that will not fall to counting alone: each needs at least one place where you follow a box through to a contradiction before you know it is out. Expert is the same ten by ten with the biggest numbers rubbed out, as many as the board can carry and still have one answer, so half a dozen boxes or more show a question mark and you work their sizes out from what the printed numbers leave over. The contradiction move hard needs once, expert needs at least six times. A fresh board is dealt every day, for nothing.

Play today's board