It'd also be interesting to explore other optimisation metrics, e.g. having common letters on the ends to allow the user to 'blindly' move the pointer to one end or the other without a need for precision.

I'm also curious if e.g. 10 shifts is twice as bad as 5 shifts, it feels to me like there's a drop-off in shifting cost after one shift.

The commonly used metric when talking about the time taken for a user to move a mouse to click on the button is log(distance/button size). So there's certainly an argument there to use the logarithm of the distance, rather than the distance.

Optimisation: Make the character row into a ring.

It would also make it easier to find the optimal layout, as a few permutations are removed.

Done[1].

That is, you have just invented the classic Dymo label maker :)

[1]https://www.staples.com/dymo-organizer-express-pro-industria...

Ah yes, in fact, why don't we go one step further and add a new button for every letter!

Such an interesting problem!

And still relevant -- at least for those of us who still have the classic Dymo[1].

Also, this pun in the article made me chuckle:

> The ComfortablyNumbered typewriter.

[1]http://juliastainton.com/2007/05/27/dymo-label-maker-cest-bo...

It would be interesting to see a two-dimensional version of this.