Logic Puzzle

I heard a brain teaser from a friend of mine the other day. I thought it was fun so I thought I’d share it here.

A king has 3000 subjects in his kingdom, both men and women. The king comes into a large amount of money one day, and decides to spread the wealth by giving $45 to every man in the kingdom who asks for it, and $60 to every woman in the kingdom who asks for it. One of every nine men and one of every twelve women request and receive their money. The question: how much money does the king give away in total?

The answer is a real, numeric figure. There aren’t any “cheap shots” in the clue, so don’t read for double-meanings or anything. If you’re a math whiz this won’t take you more than 60 seconds, but it’s fun to attempt and solve even if you’re not. Go for it! Oh, and don’t look at the comments until you’ve solved it, because the solution will be in there soon enough, probably posted by one of the proud readers who solves it.


  1. "Dookie"
    Posted January 26, 2005 at 6:37 pm | Permalink

    Fancy cancellation. 15000. Uh, unless I messed up.

  2. Posted January 26, 2005 at 8:41 pm | Permalink

    Stupid math. Use less numbers.

  3. Posted January 26, 2005 at 10:07 pm | Permalink

    Good work, Dookie. It is kinda sneaky how it works, isn’t it? You’ve just gotta have faith that it’ll be worth it to reduce the problem, and keep going, and then it just pops out at you.

  4. Posted January 27, 2005 at 12:16 am | Permalink

    Heh, pretty easy math (if you have a pen and paper, or have a good short-term memory), but you have to think for a second to realize why it works.

  5. "Dookie"
    Posted January 27, 2005 at 9:56 am | Permalink

    It’s true, the math itself is straightforward. The corollary, sorta-trick question which then reveals why the problem works is “How many men and how many women are there in the kingdom?” For simplicity, I suppose we ought to assume that, like the average family has 2.2 kids, the average kingdom can have fractional people as well. Otherwise the problem becomes discrete, but that would make Goss happy and we can’t have that.

  6. MJ
    Posted January 27, 2005 at 1:35 pm | Permalink

    Oops. I just figured out why you don’t need to know the exact number of men and the exact number of women. D’oh.

  7. POP
    Posted January 29, 2005 at 8:46 am | Permalink

    I haven’t done classic algebra for a long time, but I worked it out – $15,000. Mrs. Brown would be proud of me.

    Back when I took math, we’d only discovered and had at our disposal numbers up to 100,000, so I’m feeling pretty good.


  8. Posted January 30, 2005 at 9:41 pm | Permalink

    You silly comment-makers, you! You are all so incredibly simple-minded! You’ve failed to consider that in a fiefdom such as the one implied in the question posed, the serf tax alone would be enough to ensure that the king would end up MAKING money. And what about the Pope!? Obviously you have failed to appreciate the more significant but subtle facets of this “teaser.”

  9. POP
    Posted January 31, 2005 at 7:12 pm | Permalink

    OK, so I found my own way to do it. You have to have two equasions, so I did mine from a non-conventional view point. Shall I write them out?

  10. Posted January 31, 2005 at 8:14 pm | Permalink

    Yeah! Let’s see ’em.