Tuesday, January 01, 2013

Trust No One

Puzzling Parables
Part Three

In the third and final entry in this little series of puzzling parables we'll be looking at the strange relationship between the puzzle setter, and solver. It's an odd little relationship because while it is based entirely on trust, it is one that the setter will try to abuse mercilessly.

We've already looked at some of the rules of engagement between these two warring factions, and for the most part these are respected; but puzzle setters are, and have always been, sneaky little souls who are constantly trying to find new ways to fool you. Think of us as Kevin McCallester in Home Alone, or Jerry in those endearing cat and mouse cartoons.

Puzzle setters will always try and work around the rules, maybe by leaving out a key piece of information but inferring it's presence as in 'Night Sight' or by cramming a puzzle so full of pointless flavour that you cant see the wood for the trees - as in our very first puzzle - The G-R-Y Puzzle.

What really entertains a puzzle setter however, is to pose a question to which there is no answer. Now of course that would be cheating, so let me explain a little more what I mean with the following example.

Lateral Thinking
The Number Games

How can eleven plus two equal one?

How can twenty-two plus two equal one?

How can five plus two equal one?

Despite the fact that we haven't done much in the way of number puzzles up to now, I'm sure you can see that they can't. Clearly the puzzle setter has an extra piece of information that they are not handing over, the answer therefore lays within.

First things first, your puzzle alarm bells should be going off at the sight of numbers written as letters. It's grammatically unpleasant to have numbers over twelve written out as text without good reason. Clearly the puzzle setter is hiding something.

It could be a matter of algebraic substitution, where each letter stands for a digit, but these are hard to work out and shouldn't be your first port of call. That leaves another favourite of the evil puzzle deviser, number systems.

Human beings are hard wired to count in tens, we have ten fingers for the most part so it's natural for us. The metric system for example is based on the number ten and is the system of choice for scientists everywhere because of it's ease of use. Puzzle setters therefore love to dip into different number systems to find inspiration. That brings us back to numbers written as text again, the number system used might be more obvious with the numbers written as digits.

11 + 2 = 1
22 + 2 = 1
5 + 2 = 1

Computing uses both base 16 and base 2 number systems for various things, but these dont seem to work here as we need a variable number system, not a fixed one. Geometry has both degrees and radians to play with, which is heading in the right direction and of course there is great fun to be had with imperial weights and measures. All of these however are straying into general knowledge territory and there is still one insanely complex number system that we use every day.

The number of units making up a '10' in that systems goes 60, 60, 24, 7 or 28, 29, 30 or 31, 365, 365 and 1/4 or 366 or 52 or 12.

Tine is of course the solution, 11am plus 2 hours is 1pm; 22 hours plus two hours is one day and five days plus two days is one week.

Now, here's a completely different number puzzle where you are outright being conned. See if you can make sense of it.

Number Puzzles
A Cocktail Catch

At our Christmas Party, now reorganised after the power cut, only three people were left at the end of the night. Me, my boss and his P.A.. My boss, unwilling to end the evening took us up to the hotel bar for a nightcap.

The prices were ridiculously expensive but, knowing the awesome power of the company expenses account, we each put £10 towards a bottle of champagne.

Unbeknownst to us we had been overcharged as the bottle should only have cost £25 and that put the waitress in an awkward position, how to divide the £5 change between three of us.

She decided to tell a little white lie and told us the bottle cost £27 returning £1 to each of us and pocketing the remaining £2 for herself.

That makes £9 that we each paid plus the £2 that the waitress pocketed. That only adds up to £29 however, where is the extra £1?

Good Luck, and have a very Happy New Year!

photo credit: Experiment 33 via photopin cc

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