69^2 = 4761

69^3 = 328509

As you can see, the square and cube of 69, in base 10, contain all the digits with no repeats. In general, a nice number, in some base, is one where the square and cube, written in that base, contain all the digits in that base with no repeats.

[EDIT 12/27/22: -69 in base 10 has been brought to my attention. It technically meets my definition, but is not in the spirit of the market. I'm still thinking about how to handle this and am temporarily halting trading.]

[EDIT 12/28/22: I've decided to resolve N/A and create a new market with an improved definition, linked below. See the comments for more discussion of this decision.]

So far, this is the only nice number I know of. I suspect that there are an infinite number, but they only start appearing around base 120 to 130; I checked up to around base 30.

I discuss this more in my blog post http://tinyurl.com/confluxblog/post/is-69-unique.

Anyway, hopefully this market inspires you to do some research into finding nice numbers, or to find someone else online who has!

I may also provide mana rewards for partial results.

Close date updated to 2022-12-27 12:23 pm