bored and nerdy

[bertine]

my coworker (the fc) gave us this puzzle. i think i amazed everyone by solving it so fast. i think people forget that under this girly facade is someone that did get a degree in math and let's not forget that letter in math team.


you have $100 and you need to buy exactly 100 chickens. hens cost $1, roosters cost $5 and chicks cost $.05. You must use up all your money. (oops, i forgot this) You must buy at least one of each type. how many of each do you end up with?

also, someone come to quangs with me, i am craving an S5 so much right now.

Comments

[jayp39.livejournal.com]

2 roosters $10
20 chicks $1
89 hens $89

aren't there quite a few solutions to this? were we supposed to find the number that would give us the most chickens altogether or something?

[jayp39.livejournal.com]

d'oh, missed the part about needing to buy exactly 100 chickens...

[bertine.livejournal.com]

i was just going to tell you that. LOL

:)

[jayp39.livejournal.com]

Finally have a break from work.
Maybe I'm going down the wrong path.
Is this impossible?

If we look at it like this:
COST -- NUMBER WE GET
i.e.
$01 -c- 20
$02 -r- 10
$30 -h- 30

Then we want both sides to equal 100. Since C(h) = N(h), we don't really have to worry about that part, as long as we keep N(c) + N(r) < 100 AND C(c) + C(r) < 100. We need to find a point where C(c) = N(r) and C(r) = N(c)
The smallest N(c) we can have is 20, since we are spending a whole dollar amount and none of the other animals are less than $1, and C(20c) = $1

With N(c) = 20, we need C(r) = 20, so N(r) = 4, but C(c) = 1, so N(r) != C(c).

N(c) = 40, C(r) = 40, N(r) = 8, C(c) = 2

N(c) = 60, C(r) = 60, N(r) = 12, C(c) = 3

So you can see for every for every 20 unit increase in N(c), C(r), there's a 1 unit increase in C(c) and there is a 4 unit increase in N(r), so N(r) will never equal C(c) while N(c) = C(r)

Am I missing something?

[jayp39.livejournal.com]

nevermind, my assumption was wrong. N(c) + N(r) = C(c) + C(r).

[bertine.livejournal.com]

and i think you right. it has been a while though

[bertine.livejournal.com]

nerd. :P