# Rectangles, Explosions, and Surreals

Hi everyone! We’ll be back with a new post next week. Until then, enjoy this “explosive” post from October 2012.

Welcome to this week’s Math Munch!

What is 3 x 4?   3 x 4 is 12.

Well, yes. That’s true. But something that’s wonderful about mathematics is that seemingly simple objects and problems can contain immense and surprising wonders.

How many squares can you find in this diagram?

As I’ve mentioned before, the part of mathematics that works on counting problems is called combinatorics. Here are a few examples for you to chew on: How many ways can you scramble up the letters of SILENT? (LISTEN?) How many ways can you place two rooks on a chessboard so that they don’t attack each other? And how many squares can you count in a 3×4 grid?

Here’s one combinatorics problem that I ran across a while ago that results in some wonderful images. Instead of asking about squares in a 3×4 grid, a team at the Dubberly Design…

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1. um…u are say 3 x 4 = 12, but you used some graphing boxes to show that 3 x 4 maybe not = to 12, so i wanna ask that the nunber 3 x 4 and the boxes 3 x 4 are they the same thing? like can you compare these two things?