Yesterday, since I was feeling a wee bit impish, I published a post entitled, ‘The Black Dog and The Woods‘ and in it I set the following puzzle.
A farm house sits on a plot of land which is 200 meters square and surrounded by a wall.
Actually the farmhouse is 10 meters from the back wall and some 150 meters from the front wall and gate.
Tied to the farmhouse by a piece of rope some 300 meters in length is a black dog.
At the front of the land there is a 10 meter wide river over which there is a small bridge.
Across the bridge and only 1 meter away from the bridge is a wooded area come forest which is 200 meters square.
If the dog does not break free from the rope and there are no obstacle in its way, how far into the woods can the dog go?
(Please note that the above picture whilst pretty much to scale is not exactly to scale and is only a guide)
This puzzle really wasn’t as random as it may at first have seemed.
So Firstly in case you were doing the maths here is the relevant maths and salient points for you…
The Farmhouse is 10 meters from the back wall of the 200 square meter enclosed farm land and 150 meters from the front wall and gate.
Therefore the farmhouse is some 40 meters from front to back…
200m (length of the land) -150m (gate to farmhouse) = 50m – 10m (back wall to house) = 40m (farmhouse from front to back)
Since the dog is tied to the house the shortest amount of rope he would use to get to the front gate is 150m (farmhouse front to front gate) and the longest is 190m if tied to the back of the house. (150m from front of house to gate + 40m width of house)
So, since we know the rope is some 300m long, at the front gate the black dog would have either 150m of rope left (if tied to the front of the house: 300m rope – 150m distance from house front to gate) or 110m of rope left (if tied to the back of the house: 300m rope – 190m distance from house back to gate).
We also know there is a 10 m wide river with a small bridge over it which the dog has to cross in order to reach the wooded area and that the edge of the wooded area was 1 meter away from the bridge. This meaning that the dog would use a further 11 meters of rope in order to reach the edge of the wood.
So we know that at the edge of the woods the dog will either have either 139m of rope left or 99m of rope left depending on whether he was tied to the front or the back of the house.
The only other information that we know is that the woods come forest are 200 meters square – 200 meters wide by 200 meters across.
So since the wooded area is 200 meters square and the dog has some 139 meters or 99 meters of rope left you would think that the dog could go either 99 meters or 139 meters into the woods yes?
Well actually no he can’t. Did I mention that I was feeling impish?
Yes the dog can indeed go 99 meters into the woods but no he can’t go 139 meters into the woods.
Why? Well it all comes down to the size of the woods. We know that they are only 200 meters across by 200 meters wide. From this we know that the central point of the woods is 100 meters in from the edges.
And if the central point is only 100 meters in from the edge any distance that the dog travels beyond that point means that the dog is no longer traveling into the woods but actually traveling out of them.
And since our question was how far can he travel into the woods the 139 meters has to be wrong! And the most he can travel into the woods is 99 meters if he was tied to the back of the house and 100 meters if he was tied to the front of the house.
Of course it is not a perfect puzzle – there is of course no guarantee that the dog would go in a straight line.
But, in my defense, I did already confess to the fact that I was being very impish and I also admitted that the puzzle wasn’t necessarily that random.
In my aforementioned previous piece I likened the woods to depression or a depressed episode. Some of you very cleverly picked up on that.
Unlike the woods in our puzzle however, (the length and width and thus central point of which we know) we don’t know the length of a depressed episode until it is over.
And if we don’t know the length of the depressed episode until it is over we can’t possibly know the central point of the episode either and thus can’t really know if we are going into the depressed episode or coming out of it?
Now to some this realization might seem demoralizing even frightening – where is the structure? Where are the markers? The points of reference?
But what if we looked at it a different way? What if we said that since there is no set structure, no set markers and no set points of reference telling us where we are in that depressed episode we can decide that for ourselves and decide to be coming out of it any time we want to?
Does that sound too easy? Too radical?
Well what if it isn’t? What if it really is – in some ways just that easy?
Ask yourself this if you will, “How many times has your motivation to fight through a depressed episode been reduced by the knowledge that previous episodes have lasted a long time?” How many times, and be honest with yourself here, have you sat in a depressed episode and resigned yourself to the fact that it is going to last a lot longer – adding the words, “it always does” to your internal dialogue?
Well, who says it always does or always has to?
After all we have already established the fact that the only structure, the only markers, the only points of reference are the ones that you yourself assign or accept.
Now obviously I understand that depressed episodes can sometimes be totally beyond our control and likewise I accept that sometimes there seem to be indicators that the depression (our wooded area) is heavier or more intense. (Or thicker/denser in respect of our woods.) But who is to say that this is the middle of the depression (or our relative wood) Who’s to say that this isn’t simply another slump within the depression?
The point I am making is that at the end of the day the depressed episode (or our wooded area) is our depressed episode (our wooded area) and thus we get to have some say in how we deal with it. Whether we deal with it in the attitude of walking deeper in or indeed walking out of it.
This whole thought process and dialogue started because I myself suffered a crash and felt myself having already entered into that depressed episode.
Let’s be real here, sometimes you can be part way into a depressed episode before you realize you are in one. (Just as sometimes you can walk past several trees before you work out that it is in fact the edge of a wood you have been walking into.)
I have been putting a lot of effort into getting healthier and losing this darned weight. I have also had a lot of success and am so thankful for that since it really is so very important.
BUT I know where these depressed episodes lead, (what the centre of that wood is like), and I know how they affect me. Even putting my mental health issues aside for a moment I cannot afford to go there if I can possibly help it and I can’t afford for my physical health to suffer any more.
As I said our puzzle isn’t a perfect puzzle as there is no guarantee that the dog will go in a straight line. And of course it is not a perfect world and there is no guarantee that we can control the depression. BUT we can try and that is the important thing and we can recognize the fact that we do sometimes have a say in whether we are walking into the depression or out of it!