Impossible FreeCell?

Any fans of FreeCell out there? I find FreeCell to be a fun and relaxing mental challenge. I enjoy playing a hand or two on my iPad to unwind. I often listen to a little Pandora or I Heart Radio in the background while I work out the solution to the next random puzzle.




I've played 1620 games of FreeCell on my iPad, and I've won 1590 of them. Once I figured out that every array has at least one solution, I stick with a game until I figure out a way to win. Clearly some starting setups are more difficult than others, but this one (Fig 1) nearly cost me my 1402-game winning streak  In all of that time, I've never seen a more difficult starting setup.

Fig 1. The most difficult starting setup I have seen in over 1,600 games

What makes this setup so hard? How can one tell at a glance that this will be a tough challenge? Look at the face cards. The topmost three rows contain only 3 face cards. That means 9 of 12 are in the lower half of the array. The aces are distributed widely (columns 1, 3, 7, and 8). But more importantly, notice how high they are in the array. Face cards low and aces high spells trouble! Now, look at the fourth column. The red 10s are inaccessible, meaning the black jacks in the bottom row of columns 1 and 3 are going to be anchors for many moves.



Fig 2. The red 10s are in place, but now what?

My initial strategy involved clearing my way to the red 10s, since I assessed that bottleneck to be my worst problem. I came close to a solution here. Look at where the red 10s ended up. However, there are too few remaining moves available. This interim arrangement (Fig 2) does not have a successful outcome--at least not one that I could foresee.

 



Fig 3. Victory is in sight.

Once I got to this point (Fig 3), I knew that victory was soon mine! Can you look at this interim stage and play the remaining moves out in your head? How many moves are left until victory?

Fig 4. VICTORY! (Finally)



Yes, I finally won this game, but it was a struggle. It took me just under 3 hours over the course of several days. For me, the feeling was similar to catching the biggest marlin I've ever seen.







Calculating the "Effective Temperature"

When does 50 deg F feel like 30? What is the effect on performance for a person with skin exposed to air that feels, for all practical purposes, as if it were cold enough to freeze water? It’s one thing to consider what a given thermometer reading actually “feels like,” and another to examine the actual impact of the effective temperature on a person's skin. Heat loss or gain on the skin can change a person's core temperature enough to affect performance. Untreated, conditions like frostbite and heat exhaustion can lead to permanent damage and even death. 

This post is written with the all-weather motorcyclist in mind, but it will benefit any outdoor enthusiast who wants to understand and prepare for the effects of wind-driven heat or cold on exposed skin. I was motivated to take this project on after seeing many inconsistent charts and graphs online. Not only do the numbers not match, but there seems to be a lack of information around the impacts on performance in extremes. I also felt frustrated over the lack of awareness about the difference between "Feels Like" calculators (windchill, heat index), and effective temperature. 

I intend to create and share an online calculator, where people can type in the two variables (ambient temperature, wind speed) and get a useful response. I’d like the response to include three important pieces of information:

• an effective temperature, in deg F. This value will be higher or lower than the ambient temperature due to the effect of wind.
• a description of the impact of the effective temperature on performance. This value can be expressed in terms of minutes to frostbite on the cold side, or minutes to heat exhaustion on the hot side.
• commentary on how to mitigate the effective temperature's impacts. This can include practical tips for preventing, recognizing, and countering the described effects.

In my ongoing research, I have confirmed the need for this calculator in that nothing quite like it yet exists. This calculator will be useful for people who perform outdoor activities in extreme conditions. The actual demand for the tool remains to be seen but I plan to do some market testing to collect some data and make customer-focused improvements.

Here is how the calculator looks now. It takes the form of an interactive chart. Type in the variables, and one gets a point value for the effective temperature, as well as a description of the likely effects and some guidance about how to mitigate the effects.

Here is a more legible view of the cold (left) end of the chart. The Effective Temperature (ET) formula is given as ET (deg F) = 35.74 + (0.6215 * Temp) - (35.75 * (Wind^0.16)) + (0.4275 * Temp * (Wind^0.16)). 

And here is a closer look at the hot (right) end. The ambient temperature has a 180 def F range. The formula for ET works at the higher temperatures because it measures the effect of wind, not humidity. These results will look different from a heat index chart.

Given a calculated point value for effective temperature, here are additional results obtained: the impacts are placed in a color-coded range, the impacts are described in terms of minutes until the damage can occur, and some strategies are offered.

This is what the data entry fields look like. Type in the ambient temperature (green cell), type in the wind speed (gray cell) and the effective temperature is calculated and color-coded (yellow cell in the illustration). The color code matches the ranges and leads to information about impacts and strategies for that range.

And now you can see how the whole interactive chart works to focus on a rider's sweet spot and the risks associated with performance in areas further from that sweet spot.

There is at least one decent calculator already in existence. You can check it out at this URL. It's accurate but it leaves a lot to be desired.

•Pro

•Uses the NOAA formula

•Works for both Wind Chill and Wind Burn

•Includes conversions for Celsius and Knots

•Con

•Does not use Color Codes to describe Temperature Ranges

•Does not provide Minutes Until Impact (Frostbite or Heat Exhaustion)

•Does not offer Prescription and Mitigation Strategies

The primary objective of this inquiry in into calculating the effective temperature is to understand the impact of ambient air temperature and the wind of motion on exposed skin. Armed with this awareness, the outdoor enthusiast can better assess and manage the environmental and personal risk factors before motorcycling, skiing, running, or boating in extremes.

Thank you for reading. Please leave comments or send me an email with your suggestions.