In each issue of the Automation Notebook we feature a section of brainteasers. These are the brainteaser answers from Issue 6, 2006 of the Automation Notebook. The brainteaser questions are repeated in black. The answers to the brainteaser questions are highlighted in red with explanations. You can view the brainteasers from Issue 6, 2006 without the answers here: http://library.automationdirect.com/brainteasers-issue-6-2006/

**1. Light Weight **

The AutomationDirect DL05 PLC weighs 4.5 ounces plus half its own weight. *How much does it weigh?*

**Answer: **This riddle trips-up many people with its wording. They start with the 4.5oz and add half of that (2.25oz) to get 6.75oz. But 2.25oz is not “half its own weight” of 6.75oz.

Algebraically, we could write it 4.5 + 0.5x = x, and solve. x = 9oz. To put it another way, when you add two numbers together – knowing that one of the numbers is half the total – then you can surmise that the second number is exactly half, also.

Now, here’s another one. The DL05 PLC (most models) costs $49.50 plus half its own cost. How much does the DL05 cost? The DL05 may not weigh much or cost a lot, but it’s packed with features and offers true value for smaller automation projects!

**2. A Puzzling Journey**

I’ve been warned about a journey I must take in the next few years. The details are very sketchy, but I’m told that the whole trip can be mapped out using a familiar grid pattern. This is a grid everyone knows about and uses, but no one can alter.

I’ve been given starting coordinates of 7, 7, 7. First, I’m to travel 398 grid units to position 8, 8, 8. Then I must continue in the same direction another 397 units to 9, 9, 9. It’s impossible to retrace my path, so I will travel another 396 units to 10, 10, 10. I’m only allowed to spend one day at each stop.

*What is this grid, and how long will my journey last?*

**Answer:** The grid is a standard calendar, and the journey (through time) will take 3 years 3 months, and 3 days (1191 days). Beginning on July 7 th , 2007, and ending on October 10 th , 2010. I hope you can join me 😉

**3. SuDoku**

Oops, we goofed! There was a mistake in the SuDoku puzzle in the printed version of our magazine. The bottom right box contains a “9” where there should be a “3”. Our sincere apologies. The corrected puzzle is below:

SuDoku is somewhat like a crossword puzzle, but it uses numbers instead of letters.

The rules are simple: *Fill in the empty squares so that every row, every column, and every 3×3 box contains the digits 1 through 9.*

No math is required. Logic is all you need.

Here is a “mild” SuDoku…

Before you look at the SuDoku solution, would you like to download a *C-more*touch panel project that will help you solve this puzzle? You must have the free *C-more* Demo Software also (click here to download the demo).

The *C-more* touchpanel hardware is not required – you can work the puzzle using the simulation mode of the *C-more* software. The simulation mode is just one of the many exciting new features of our *C-more* Touch Panel Operator Interface.

Here are a few hints, the full solution is below.

Consider the square in the third row, sixth column (circled, with checkerboard pattern). Notice that there are already 4’s in both the top row (row 1) and the second row, and that there are also 4’s in the 4th and the 5th columns. You can logically determine that the only place for a ‘4’ in the top middle ‘mini square’ is the circled location. This technique is know as “slicing and dicing”. Now consider the circled square in the upper left (row 1, column 1). By checking across row 1 and down column 1, it becomes clear that ‘8’ is the only number that can be used in this location, without duplicating one of the existing numbers in row 1 or column 1. This method is called ‘elimination’. The other shaded boxes in the puzzle above can all be solved by studying the “given” clues. Once you have those filled in, additional boxes can be deduced, until the puzzle is solved. There are several other techniques that can be used to help solve Sudoku puzzles. Pick-up a book of puzzles, or Google “Sudoku” for a wealth of information and additional puzzles.

**Here is the full solution:**