Camino del Norte part 12

As usual, before getting to my story of the Camino del Norte, I present my weekly logic puzzle.

Logic Puzzle

A token is on the upper left square of an 8x8 chess board. It may travel only one square at a time down or right. How many different paths lead to the square in the lower right corner of the chess board?

Camino del Norte part 12

This chapter in my adventure shall cover the four-day section of the Camino del Norte between Ribadeo and Parga. I took six days to travel the section between where the route leaves the north coast in Ribadeo and when it joins the Camino Frances in Arzua. This chapter 12 shall cover the first four of those six days.

Day 18 (April 4)

This first inland day was not very noteworthy. Mario was gone before I got up, again, so I walked by myself all day. There was not another pilgrim to be seen. It was a comparatively long day at 28.6 kilometers.

My lodging that evening was at the Castelos Albergue in Lourenzá. Out of 26 beds, I was one of only three pilgrims. The other two I barely saw and never spoke to. The host was barely there as well. The town was rather nice. Not as much as Ribadeo, but still one of the better ones. I dined on Galacian octopus again, which I can never get tired of.

I tried to boil some eggs for the next day but couldn’t get the stove in the Albergue to work. Instead, I tried to microwave them. Big mistake. I don’t even want to talk about it, except to say I was glad nobody else witnessed it or the cleanup.

Day 19 (April 5)

This easter Sunday I got an early start, leaving with just enough light out to see. About two hours later, I surprisingly caught up with Mario, who I hadn’t seen in two days. Mario walked faster than me, but took longer breaks, I think to conduct business via his phone. We walked together for a while, but I eventually cut him loose as I knew he probably wanted to walk faster than I liked to go.

A point of conversation before we parted company was which way to go between the towns of Mondoñedo and Abadín. Option 1 was 12.9 kilometers via a steep and lonely route with no services. Option 2 was a more scenic18.3 kilometers that passed through a few small towns, one of which had an Albergue.

Mario and Sebastian (who I met on day 13) chose the longer option 2. I went with option 1. There was 480 meters of elevation gain over 5 kilometers. That was the longest sustained climb of the Camino. At least it was nice weather, although perhaps a bit too hot. This was the only portion of the Camino on which I took more than one bottle of water, which I needed. After the climb, the route followed a ridgeline amongst a lot of windmills. The only sign of civilization I saw were the many windmills and one car that probably was up there to service thm. This dry, rugged and unpopulated section of the Camino reminded me of the Trans Catalina Trail, which I have done three times.

Eventually, I made it to Abadín, beating Mario. The Albergue host was very nice and was amazed by my magic tricks. As mentioned, it was Easter, so most businesses were closed. I ended up getting bread, wine and cheese again at a convenience store. Mario was fussier about his food than I was and walked further to buy all the makings of a good sandwich. When he got back to prepare it, he was rebuffed by a lack of olive oil in the Albergue kitchen. When I suggested he use the available peanut oil instead, he was shocked. As I recall he said, “No self-respecting Italian cooks with peanut oil.”

In the end, he was generous sharing what he made and there was a nice informal shared meal among the four or five pilgrims there. A nice way to spend Easter, although nobody brought it up. I think Jesus would have approved.

Distance covered day 19 was 21.8 kilometers.

Day 20 (April 6)

Day 20 was a comparatively short and easy 21.8 kilometer day. As usual, I walked by myself. The Camino went through only two very small towns.

I arrived early at my destination for the day, Vilalba. There I reunited with Mario and Sebastian. Mario and I had a nice lunch. I offended him a second time by my lack of dining standards. As I recall, his words were, “As an Italian, it hurts my eyes to see you eating fish with red wine.” He had to get back to Italy for an important meeting only to return to the Camino the following day after that.

The town of Vilalba was fairly large but not nearly as scenic as other cities I went through along the coast. Back at the Albergue a young woman dressed like a hippy and I suspect under the influence of some kind of drug offered the entire place some eye candy. Meanwhile, I got to know Sebastian better. He asked me how Americans could have elected who we did for president two years before. That led to a three-hour conversation. Fortunately, there was plenty of time for it as we had nothing else to do.

Day 21 (April 7)

This was another rather uneventful day on the Camino. 5.2 kilometers past Baamonde, the route split again. I chose the north route, which was shorter, but probably not as scenic. Yet again, I walked alone and saw no other pilgrims.

My destination for the day was the very small town of Parga. There I found an outstanding new Albergue called the Natura Alojamiento. I got there just in time as it started pouring rain about ten minutes after my arrival.

This was probably the most luxurious Albergue I have ever stayed at. As often is the case in small town, the building I’m sure was intended to be a private home. The woman who ran the place treated me as if I were one of her first guests ever. She asked for my suggestions on how to get mentioned in the guidebooks and apps. I mentioned other Albergues putting up advertisements. She said she tried that but competing Albergues took them down.

While relaxing in the living room Lena from day 6 walked in with her apparent boyfriend who joined her somewhere along the way since I last saw her. He was a strapping young lad who spoke perfect English. I got along much better with him than I ever did with Lena.

The hosts offered an outstanding dinner. One of the best Albergue meals I had on the entire trip. Sebasian was also there, but declined paying the extra money for the dinner. He seemed to be in a bad mood about something. This would be the only time I saw members from my groups from day 6 and 13 at the same time (Lena and Sebastian), although I never saw them speaking to each other.

My milage for day 21 was 26.4 kilometers.

Logic Puzzle Answer

3432

Logic Puzzle Solution #1

Note that to get to any square the token must come from either the square above it or to the left of it. That said, we know there is only one path leading to any square on the left column or top row. Then, the number of ways to get to any other square is the sum of the cell above it and to the left. The following table shows the number of ways to get to the lower right cell is 3432.

1	1	1	1	1	1	1	1
1	2	3	4	5	6	7	8
1	3	6	10	15	21	28	36
1	4	10	20	35	56	84	120
1	5	15	35	70	126	210	330
1	6	21	56	126	252	462	792
1	7	28	84	210	462	924	1716
1	8	36	120	330	792	1716	3432

 

Logic Puzzle Solution #2

The token will have to make seven steps down and seven steps to the right. The total steps required is 7+7=14. The question is how many ways can he arrange these 14 steps? Number these 14 steps 1 to 14 according to the order made. How many ways can you choose 7 out of these 14 steps to move down?

The answer can be expressed as combin(14,7), to use Excel notation. In other words, 14!/(7! * (14-7)!) = 14!/(7! * 7!) = 87178291200 / (5040 * 5040) = 3432.

Acknowledgement

I would like to credit Presh Talwalkar with the ‘MindYourDecisions’ YouTube channel for the inspiration for this problem. It can be found in the video titled “Can You Solve Apple's Paths On A Grid Puzzle?”

Written by: Michael Shackleford