The funnest thing about interviewing at Microsoft are the famous (or 
infamous) "interview questions", of which you're likely to get at least 
one per interview. A classic example is:

You have three closed barrels in front of you, one filled with black 
marbles, one filled with white marbles, and one filled with a mix of 
black and white marbles. You also have three labels, one to a barrel, 
reading "Black", "White", and "Mixed". You are told that each barrel has 
the wrong sign on it. You are allowed to draw one marble from a barrel. 
What is the least number of marbles you can draw to put the signs 
aright, and from which barrel(s) do you draw it/them? *(Answer below)

Here's one I just got this afternoon that I hadn't heard before, though 
I'm pretty sure it's an old question:

You wish to market a climbing chain consisting of some lengths of chain 
that can be joined together by carob-beaners (removeable links). Regular 
chain links are dirt-cheap; carob-beaners are very expensive. You want 
to market a chain set that can be used to create a chain of any length 
between one and twenty-one links, without any "left-over" links. (That 
is, you must have exactly 21 links in your kit, including 
carob-beaners.) What is the least number of carob-beaners you must 
include in the kit, and what are the lengths of chain you must also 
include? **(Answer below)


(SPOILER: Answers below)

* Draw one marble from the barrel labeled "Mixed", since you know it's 
either the black or the white barrel (it isn't mixed -- the labels are 
all wrong). Put the appropriate label on that barrel, move the remaining 
"Black" or "White" label onto the now-unsigned barrel, and put the 
"Mixed" label on the remaining barrel.

** Short answer: Three carob-beaners, four lengths of chain as follows: 
7 links, 7 links, 3 links, 1 link. Longer answer: You can quickly show 
that two carob-beaners is insufficient for making the correct 
combinations, since you must then have a three-link chain (your 
carob-beaners only combine for two links), and then a six-link chain 
(your three-link chain and carob-beaners only combine for five links). 
Two carob-beaners will only allow you to join a maximum of three lengths 
of chain; so your third length has to be 21 - 6 - 3 - 1 - 1, or ten 
links long. However, you have no way to make a nine-link chain: 6 + 1 + 
1 = 8, and 6 + 1 + 3 = 10 (you can't directly join the six-link and 
three-link chains without a carob-beaner). So (Point #1) you will 
require at least three carob-beaners. Now, if you have three 
carob-beaners, that means you can have up to four lengths of chain. But 
how do you go from a 20-link chain to a 21-link chain? You have to add 
on a single link. That last link is either one of your carob-beaners (in 
which case you can only have three lengths of chain, not four), or else 
you have to have a one-link length of chain. You can quickly show that 
three carob-beaners and three lengths of chain won't work, so (Point #2) 
one of your four chain lengths must be a single link. Once you see these 
two points, you can play with the combinations and figure out the chain 
lengths that will allow you to do it with three carob-beaners. If anyone 
has insight how to arrive at an answer faster, please do tell.

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