# Puzzle 19: Block Party

...And you're invited!

Puzzle on left, solution on right rendered in festive orange. (The light yellow circle is a solving aid referenced in my sample solution.)

The object is to take the given grid and divide it into rectangles such that each contains exactly one numbered cell denoting its area.

Yes, ladies and gentlemen, that's it. No nodes, no ciphers, no values to fill in, no odd wiggly shapes - just simple rectangles. Why should a party be complicated, right? I'm not even giving a numbered list of instructions for this one - that would be too tedious.

If you're finding the sample puzzle more frustrating than fun, then here's the recipe for the appetizer:

(Start of sample puzzle solution)
There are three basic things to look for to solve a Block Party puzzle. I could give them fancy names, but hey, it's an informal party, so I'll just save those for Wikipedia or something. Anyway, take a look at that '4' in the upper-right corner. There's only one way it can be part of a rectangle. It can't be four-in-a-row across - the '6' is in the way - and it can't be a two-by-two-square - a '2' blocks that. So it must be four-in-a-column down. That's the first thing to look for: numbers that can only be boxed in one way.

After walling in that '4', look at the bottom-right cell of the grid. Since it needs to be part of a rectangle with a number, it will need to be part of a one-cell-tall rectangle running along the bottom row. How long? Well, since it needs a number, it's going to run across until it finds one, and then that number is how long it must be. This is the second thing to look for: unnumbered cells that can only be boxed in one way. If you look carefully, you'll see the cell to the left of the '4' on the top row also can only be boxed in one way: with the '2' right below it. If you also take care of the '2' in the bottom-left corner, that's four of the seven rectangles in the puzzle figured out already.

Now look at that '6'. There are two ways it can be satisfied, but those two options overlap. Either way, it's using the top-left corner cell, its own cell, and the cell below each of those. Since the '6' is using those, no other number can. I tie these cells together by drawing a circle across the edges of those cells; you may prefer lines connecting them, or shading things in, or whatever else. This is the third thing to look for: unnumbered cells tied to a particular number. At any rate, by linking the cell below the '6' to the '6', we find that the '3' now has only one option left! From there, the next step should look very familiar, and it proves to be the last. That's it! Simple, right?
(End of sample puzzle solution)

Enjoy. Comment. Send in solutions. AND NO SPIKING THE PUNCH BOWL!

♥ - ZM

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