Kaidoku #72 & Interesting Numbers (with bonus number puzzle!)
Kaidoku #72 (PDF) | Java applet | JPZ (get Crossword Solver)Have you ever heard the “proof” that there are no uninteresting positive integers? It goes something like this: let U be the set of uninteresting positive integers. Now if U is non-empty, it has a smallest element … but that number is then interesting, for being the smallest uninteresting number! Thus U must be empty, so there are no uninteresting numbers.
Well, the proof is silly but the sentiment is true, at least for a mathematician like me. Take today’s number, 72. Why, it’s the smallest number non-trivially representable as xy*yx; specifically, 72=23*32. Not bad, right? Hey, speaking of integer powers, here’s a number puzzle for you – my age is an integer power and so is my wife’s. My wife is four years older than me. How old are we?
Anyway, if you did Matt’s contest last week you probably know why I have this stuff on the brain. Anyway, enjoy today’s puzzle, and we’ll see you Thursday!
February 8th, 2010 by
Alex | tags: Kaidoku
36 and 32. (and by “integer power,” i assume you mean n > 1.) i wonder how one solves a problem like this other than by inspection? well, i guess the easiest way is to remember that you recently turned a billion.
you really are trying to trick me with your vowels, aren’t you? today there were so many terminal Is. i’m lucky that my E guess turned out to be right, and then ACCESS jumped right out at me.
This one’s Matt’s, but yeah, DAIQUIRI and BIKINI next to each other = mean.
You got me interested on how to find the general solution to a problem like this, so I looked it up … and there doesn’t seem to be much hope of solving something like that. I wonder if there are any other solutions at all? (I would venture to guess that it’s doubtful.)
ACCESS was my access point too, although I briefly considered ABBESS too before tossing that out. Once that word was broken, the rest fell nicely. With the I’s in place, DAIQUIRI seemed like a safe (and tasty) bet.
You know, I have to admit to briefly thinking, “Hey, x + (x+4) =” and then stopping right there, realizing I was just having a combined middle-school math team and standardized testing flashback, neither of which would help much there.