zotmeister | 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

Flat | Top-Level Comments Only

Depending on how literal-minded you are, you may want to alter the rules to read, "The object is to take the given grid and divide it into rectangles such that each contains exactly one numbered cell, which denotes its area." The difference is the addition of the comma. Without it, literal-minded (or smart-alecky) solvers could respond by creating rectangles with several numbers, exactly one of which denotes the rectangle's area, and several which do not denote its area.

Unnecessary, and I'll let you figure out why. (It involves arithmetic.) - ZM

I wouldn't say that... Suppose I wrote in the number 225 in the corner and declared that I had finished?
I have a hunch that Avenger is an engineer too? :)
-grz

Read the instructions again: the objective is to take the given grid... All that I've empowered the solver to do is divide the grid, not add to it. - ZM

No, I'm a smart alec. Common mistake. Though for the record, I did spend a year in computer science.

I sent the answer to this, and to all the previous puzzles, to
the email shown on contest page. If that is not the correct
place, where should I send it; if it is, it may be a good idea
to write down after every puzzle where to send answers, though
it may be there and I din't notice.

--yyw

Sorry about that. Yes, you sent them to the right place: I used to say that my email address is on my User Info page (it still is), and it's the only email address I have (or presently want). I should be more explicit for the newcomers.

I glanced at your solutions, but haven't verified them all yet. Actually, I've gotten quite a few solutions to this puzzle, some from new solvers. I'll try to get them looked at and responded to quickly. After all, I wouldn't post my next puzzle (which is already finished) until I've finished picking up after this one. [Parties can make such a mess, or so I've seen on television.] - ZM

Wow - where do you all COME from?! I've already received NINE solutions, easily the record turnout. I guess it was a popular party!

Apologies, however, to the one that thought it was a toga party: for future reference, I have no Adobe software on my new computer and I intend to keep it that way. One person sent me a .pdf; I'll get around to opening it on my work computer eventually, but I prefer straight graphic files when possible.

Congratulations go out to (in chronological order): groza528 (a newcomer debuts with a first-solve!), avenger314, shack_a_nerd, GLmathgrant, Craig Kasper, Alex Cobian, yyw (who also sent a full backlog of solutions - now there's a trooper), and Tahnan. All received party favors.

And now, the punchline: I only posted this puzzle so that I can post the next one. Party's ending - getting back to business shortly. - ZM

Puzzle 19: Block Party

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where to send solution?

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