tower power

[David Ash]

Just to add to the collection of problems we are collecting in parallel with our overall vision taking shape:

What is the last digit of [math]7\uparrow\uparrow 2022[/math]?

Here I'm using Knuth's uparrow notation so I'm asking what the last digit of 7 tetrated to 2022--a power tower of 7's of height 2022.

This problem has the advantage that any large power tower of 7's will have the same answer so it will work even if we don't actually use the problem until 2023 or later.

[David Ash]

So a meta-question arises--and part of my purpose in posing the problem was to raise the meta-question if appropriate:

How do we express mathematical notation in Google Groups? I've never known how to do so and this will be a frequent need of ours on here if this project gets going in earnest.

[Istvan Lauko]

Not convenient to do it inline (unless you want to write and read formulas in TEX). Probably GG is  not the best tool for us, but readily available and  this is not an insurmountable problem. You can attach a file (e.g. pdf, tex,...), an image, or put in a link.

With those choices we can live.

[David Ash]

Thanks István! I guess that gets at part of my question--is it possible to write math formulae directly in TEX within GG? Or would we need to do it elsewhere and then embed the pdf, image, link, etc in GG? I agree that we can live with either option, esp for now, but just want to fully know what those options are.

[Istvan Lauko]

No inline tex compiling --- that "unless you want to write and read formulas in TEX" was just a misplaced wisecrack. Only posting files generated elsewhere.

[t...@bellefleurbooks.com]

Dear Istvan:

This is an interesting problem. The only part I recognize is "tower
power," since I am unfamiliar with the software, but this term is enough
information to understand what the question means.

The answer is easy enough to compute. It is a little tricky to prove
rigorously, since you have to use modulo twenty, so it is a good
problem. If you do not ask for a proof, a contestant may do the
computation modulo ten instead and luck into the correct answer, by
mistake.

Sincerely,

Tom

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