I don't know about you, but--like many engineers--I can easily be distracted by a logical conundrum. For example, some time ago, a friend interviewed for an applications engineer job. He was given a test to complete, and one question stumped him. At first, this appears to be deceptively simple. We start with a black box with three inputs--A, B and C--and three outputs (see below). The outputs, which we may name !A, !B and !C, are the logical inversions of the inputs.

The idea is that you have a "bucket" of primitive logic gates that you can connect together in any way you like so as to generate the required outputs. The trick is that, although your bucket contains an unlimited number of two-input AND, OR and XOR gates, it contains only two inverting NOT (or INV) gates.

I can't tell you how many hours I've whiled away at this, spending 10 minutes here and 10 minutes there as a new possibility strikes me. Sometimes I think this is a trick question, and the answer is "It can't be done." Other times, I feel as though I'm poised on the verge of a solution based on manipulating the differences between ... but no! Why should I ruin the fun for everyone else?

The reason I thought to mention this puzzle is that I recently joined an interesting Yahoo group called "How Things Work" (http://groups.yahoo.com/group/ howthingswork/). This group features discussions that morph from one topic to the next. Suffice it to say that if you want to know how to do something weird and wacky, someone in this group will be able to regale you with his or her experiences in this area. Anyway, one of the members recently posed three logical conundrums that he says were cobbled together from postings to the "sci.math" newsgroup (Problems 1, 2 and 3, at left).

In each case, the problem starts with a simple premise, such as "a = b." It then progresses through a series of steps that each appear to be logical in and of themselves, and yet the end result, such as "2=–1," is obviously incorrect. I just know I'm going to have fun with these.

If you have solutions to any of the above (especially my black-box problem), feel free to drop me a line and let me know at max@techbites.com.

Clive (Max) Maxfield is editor of Programmable Logic DesignLine, an EE Times sister Web site (www.pldesignline. com), and author of How Computers Do Math (www.DIYCalculator.com).