07/27/2025

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07/21/2025 to 07/27/2025

Tuesday morning Andrew left for the annual Deer River Band Camp! Unfortunately, it rained most of the day. I picked up our two lawn mowers from Ace Hardware, luckily, they just needed some minor repairs. In the near future, I would like to transition to an electric mower.

On Wednesday, the marching band had to come home from Deer River early because the field was absolutely soaked from all the rain we have been getting. They will continue with the camp in Grand Rapids sans camping overnight.

On Friday, for Steve’s 73rd birthday, Andrew, Tiffany, Debra, Steve, and I, traveled to Gilbert, MN. We visited Lake Ore-be-gone mine pit which is popular for SCUBA diving, swimming, and camping. We then ate dinner at The Whistling Bird which is known for Caribbean flavors. For an appetizer, we had Bacon Wrapper Shrimp Skewers & Firecracker Cauliflower. For a cocktail I had a Rum Runner and my main course was the Jerk Platter - chicken, bacon-wrapped shrimp, and pork tenderloin. Steve had the Seafood Stuffed Salmon that had a delicious hollandaise sauce, I will getting that the next time we visit.

Side note: On August 13th, 2016, after visiting the Soudan Underground Mine, we stopped and ate at the Whistling Bird. I would love to revisit the mine, here is a picture of us when the Neutrino Lab was still there.

☕️ & Math

During the week, I was trying to find the odds that the last four digits of one known fixed sequence of numbers would match the last four digits of another different sequence of numbers in a group. Unfortunately, I didn’t ask myself the question correctly and spent a lot of time figuring out the probability of a shared match, also known as the Birthday Paradox. Nonetheless, I found The Birthday Paradox to be quite interesting. Consider the following question, how big of a group of people would you need for there to be a 50% chance that any two people share the same birthday. Out of 365 possible birthdays, turns out you only need 23 people! It is called a paradox because it defies our intuition. If you asked most people how big of a group it takes to have a 50/50 chance any two people share the same birthday, most would pick half, 183, not 23. Human intuition about probability is flawed. The following is the Birthday Paradox Formula.

n = 23 d = 365 \[P(\text{shared}) = 1 - \prod_{k=0}^{n-1} \left(1 - \frac{k}{d} \right)\]

As I mentioned before, I needed a formula for a fixed match, enter the Fixed Match Probability Formula.

n = 7,000 d = 10,000 \[ P = 1 - \left(1 - \frac{1}{d} \right)^n \]

If you just need a quick approximation, you can use e^-n/d, accurate for large n, small 1/d.

A four-digit number has 10,000 possible different combinations. My group size is 7,000. The odds that the last four digits of one known fixed sequence of numbers would match the last four digits of another different sequence of numbers in a group of 7,000 is ~ 50%. If I had incorrectly used the Birthday Paradox, the probability approaches 100%.

🔗 Links

An interesting guide that shows you how to read a QR code without a computer.

An intuitive guide to exponential functions, Euler’s Number!

End of blog. Thank you for reading!