In a prior post I asked the following question:
find x,y,z positive natural numbers such that the following is true:
$$ \frac{x}{y+z} + \frac{y}{x+z} + \frac{z}{x+y} = 4. $$
I first saw the question in a more fun way:
I did not put the answer in the post (should I have? That was the meta question.)
The question has an infinite number of (x,y,z) that work, so I’ll just give the least one:
x= 154476802108746166441951315019919837485664325669565431700026634898253202035277999
y = 36875131794129999827197811565225474825492979968971970996283137471637224634055579
z = 4373612677928697257861252602371390152816537558161613618621437993378423467772036
1) For details on how you could have found the answer see here. Or watch a YouTube video on it here.
2) Did I really expect my readers to get this one? Note that I posted it on April Fools Day, though it is a legit problem with a legit answer.
3) The image that says that 95% of all people couldn’t solve it—I wonder what their sample size was and where it was drawn from. I suspect that among mathematicians 99% or more can’t solve it.
4) Comments on the comments I got:
a) Austin Buchanan says that Wolfram Alpha says NO SOLUTION. I wonder if Wolfram Alpha cannot handle numbers of this size.
b) Anonymous right after Austin had a comment that I MISREAD as saying that they found it using a python program. I asked that person to email me, and it turns out that NO– they recalled where to look (on the web I assume).
c) Several commenters solved it by looking at the web. Math Overflow and Quora had solutions. So did other places. This may make the meta question should a blogger post the solution a moot point for a well known problem. If you get a problem off the web its quite likely its well known, or at least well enough known, to have the answer also on the web. If you make up a problem yourself then its harder to tell.
5) I think its a very hard problem to solve unless you have the prior KNOWLEDGE to solve it, so it would not be a good math competition problem.
6) The cute pictures of fruit in the presentation of the problem makes it LOOK like its a cute problem. It not.
7) Only one comment on the meta question about should a blogger post the solution at the same time as the problem (There were more comments about the unimportant question of whether 0 is a natural number.) The one comment says that a blogger SHOULD NOT – let the reader enjoy/agonize for a while. I agree.
8) Determining if a given math problem is interesting is a hard problem; however, that will be a topic for another blog. (Tip for young bloggers, if there are any (blogs are so 2010): If you do ONE idea per blog then your blog can last longer.)