## Testing solutions to the 100-prisoners puzzle.

Both Matt Parker and the Youtube Veritasium channel have reviewed the surprising best practice for the 100 prisoners puzzle. The puzzle is a way to find a solution that will let the prisoners win with the most probability. If you have not seen this already please see the video here before some spoilers below.

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## Happy Pi Day 2022

Once again it is Pi day, a great time to make pie – or order a Pizza or Pie (check if your local restaurants have a special Pi day deal ðŸ™‚ )

This year Pi day comes on a Monday, which hasn’t happened since 2016! There are some interesting tricks to calculating what any given day of the week was, and I’ll leave you with a video that James Grime published with some math tricks for the day of the week for any given date:

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## Happy Twosday! and a Surprising Pi trick

In Ben Sparks’ video he shows a very interesting trick. On a decimal angle calculator run:

sin(1/5555)

If your calculator has more than the standard Ubuntu calculator’s digits of accuracy you could add even more repeating 5’s. The answer is approximately PI with extra zeros…

0.000003142

Since today is Twosday (2-22-2022 in any date format), here is a similar Tuesday math trick for the Python console:

```from math import sin
sin(22/700000.0)
```

It is also .0003142… or approximately Pi!

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## Sum/product of consecutive numbers and other math shortcuts

If you have studied some of the old SAT questions at some point you may have gone through questions like –

4 consecutive numbers sum to 166. What is the product of the numbers? or…

3 consecutive even numbers sum to X. What is their product?

The way the tutors and the online tutorials show seems to always be to algebraically solve this – for example 4 consecutive numbers would solve x+x+1+x+2+x+3 = 166, collect terms and solve…

However there is another way that works for this and works for other similar problems.

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## Slide rule enters the 21st century

Some time ago I came across this online tool in a newsletter article – this is a very cool slide-rule-emulator that will not just let you move two slides, but actually slide it for you as you run an equivalent digital calculator calculation to the right!

If you haven’t ever used a slide rule before, it works on properties of logarithms, and the principle that log(a)+log(b) = log(a*b). Now it wouldn’t be very interesting to just have two normal rulers together, as sliding and adding would just let you do problems like 5+5 = 10 or 50+50 = 100 if you scale the numbers. With logarithmic scale, the spacings are off and it allows you to do multiplication in adding the numbers.

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