Wow, no one took a stab at this one.
Maybe it will help if I show how the easy one is done. The problem was to make an equation using only the following: 2, 3, 4, 5, +, =? (Each digit should be used only once.)
The answer is 4+5=32
(In case that doesn't show up on your screen correctly, the answer is 3-squared.)
(Okay, I just realized how hard it is to do superscripts in a combox. The tag is SUP. This was probably a poor puzzle choice for a blog.)
The tougher problem was to make an equation with 1, 2, 3, 4, 5, 6, +, =, with no more or less than 2 digits in each part of the equation, and each digit only used once. (eg: [2 digits] + [2 digits] = [2 digits])
Update: Another way is to represent exponents as words: square, cube, zenzizenzic (fourth), surfolide (fifth), zenzicube (sixth), second surfolide (seventh) and Zenzizenzizenzic (eighth).
It has the benefit of being completely outmoded and wonderfully obscure, which are always nice features for me. They were created by the man who invented the equal sign. I know what you're thinking: "Someone invented that?" Why, yes he did. Apparently "=" was his only flirtation with brevity and clarity.
Sorry. Tuesday was not my lateral thinking day. Love the math and word puzzles, though.
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