Arches National Park

Logic Puzzle

The goal of the following puzzle is to find the flaw in the following argument that 1=2:

Let a=b

a² = ab

a² - b² = ab - b²

(a+b)(a-b) = b(a-b)

a+b = b

a+a = a

2a = a

2 = 1

Arches National Park

Despite Arches National Park being in my own backyard for 24 years, this was my first visit. I spent two nights at a nice AirBnB in MoabMarch 31-April 2, 2025.

The park began requiring reservations to get in beginning April 1. My first day visiting was the last day in March, so I didn’t require one. The line at the gate was about 20 minutes long. It was my goal that day to see as much as I could along The Windows Road and Delicate Arch Road, which are two sideroads from the main Arches National Park Road. The first point of interest, as emphasized on the park map, was Balanced Rock, which is easily seen from a pullout off the main road. There is also a short hike going around it.

After that, my main goal of the whole trip was to see Delicate Arch, also known as “license plate Arch,” because it appears on the majority of Utah license plates. As you may know, I am an avid license plate collector. I have been taunted to visit every time I saw one of these license plates around Las Vegas, which was often.

The hike to the arch is about two miles each way and moderately up hill on the way there. There are lots of tourists like me who evidently made it a priority as well. At the arch, a line formed to take pictures directly under it. Despite it being very touristy, if you have only one day in Arches National Park, I would see it.

After the Delicate Arch I did a about a one-mile loop trail, which went by North Window Arch and Turret Arch.

My full day in Moab began with a visit to petroglyphs known as the Birthing Rock. It is located right off of Kane Spgs (sic) Road with plenty of parking. Then it was back into the National Park, where I had a entry reservation between 10 and 11AM. By the way, such reservations must be obtained through recreation.gov. I would estimate the wait this time was about 15 minutes.

The main goal of the day was to do the eight-mile trail in the Devils Garden section of the Arches National Park, which begins at the end of the paved road. I estimate it is about a half-hour drive from the visitor center to the parking lot. The main attraction of this section of Arches is the Landscape Arch. At a span of 290 feet, it is the largest natural arch in North America and fifth in the world (behind four other arches in China).

It was my intention to make it all the way to the Dark Angel rock formation, but it started snowing, so I turned back a little early.

My final day I did about a four-mile hike (round trip) outside of the park to see Corona Arch. It was recommend to me by the woman who hosted my Air BnB and it was a good suggestion. The trail passes right by Bowtie Arch. The pictures speak for themselves.

I would also like to put in a good word for the city of Moab itself. Yes, Moab is very touristy but it still maintains a friendly charm. In the heart of town, you will not see many chain stores or businesses, in fact I think none. Especially good restaurants were the Jailhouse Café for breakfast and the Desert Bistro for dinner. Both are highly recommended by me.

The Moab Information Center has a nice and free booklet of lots of hikes and activities to do in the Moab area outside of the Arches National Park. One could easily spend three full days in Moab and have plenty to do. I wish I had more time to spend there and am eager to return to do more exploring outside of the park. In closing, I had a great time in Arches and Moab and am already eager to return.

Logic Puzzle Solution

The flaw in the argument is this step:

(a+b)(a-b) = b(a-b)

a+b = b

Since a=b, a-b=0. It is not kosher to divide by zero in math. If you must, we get 2∞ = ∞, which is true.