In honor of today’s uniform date, a quick puzzle: using six ones along with the basic arithmetic operations and exponentiation, write expressions equal to the numbers 0 through 11.

(Before I begin, the WolframAlpha blog has 11 ways the number 1 can be used to create some interesting mathematical results. I now know, for example, that an 11-sided polygon is called a hendecagon).

Ok, I got stuck on 11, which was my original goal. I can do it with some inelegant tactics (e.g. the ++ operator from some programming languages), but I couldn’t figure out a way under my original constraints. Any thoughts? Or any other methods for getting the numbers from 0 to 10?

Just wondering, for 9, wouldn’t the simple thing to do be (1+1+1)(1+1+1)? For 3, you could have just done (1+1+1)x1x1x1 or something simple like that.

P.S. Did you make a wish at 11:11:11 today? (I thought that I would get another one in a little under an hour, 11:11:11 pm, but I guess that wouldn’t be as official, as it wouldn’t be the eleventh hour of the 24-hour clock.)

For 1, I could have just multiplied six ones together, but I was trying to be a little clever with some of these.

I failed to make a wish at 11:11:11. I was not teaching a class that period so I didn’t have my students constantly reminding me that a wish time was coming up!