Brain Teasers:

Teaser
1. You are given a scale which you are to use to measure eight balls. Seven of
these balls have the same weight: the eighth ball is heavier than the rest.
The scale does not indicate the weight of a particular object; it is a scale
which tells you which of the two sides being weighed is heavier (like the
scale that lady of justice statue holds up). So, for example you could place
one ball on each end of the scale. If ball one was heavier than ball two, it
would tip in ball one's direction; if ball two were heavier, it would tip in
ball three's direction; if the balls were of equal weight, the scale would
not tip at all. What is the minimum number of weighs you could perform to
find the heaviest of the eight balls?
2. Imagine, now, that you have seven balls of unknown weight, given that six
are of the same weight, and the seventh is heavier than the rest. Using the
same scale as described above, what is the minimum number of weights you
could perform to find the heaviest of the seven balls?

3. Imagine that you have 26 constants, labeled A through Z. Each constant is
assigned a value in the following way: A = 1; the rest of the values equal
their position in the alphabet (B corresponds to the second position so it
equals 2, C = 3, etc.) raised to the power of the preceding constant value.
So, B = 2 ^ (A's value), or B = 2^1 = 2. C = 3^2 = 9. D = 4^9, etc., etc.
Find the exact numerical value to the following equation:

(X - A) * (X - B) * (X - C) * ... * (X - Y) * (X - Z) =0
4. And finally, the hum-dinger: There are four people who need to cross a
bridge at night. The bridge is only wide enough for two people to cross at
once. There is only one flashlight for the entire group. When two people
cross, they must cross at the slower member's speed. All four people must
cross the bridge in 17 minutes, since the bridge will collapse in exactly
that amount of time. Here are the times each member takes to cross the
bridge:
Person A: 1 minute
Person B: 2 minutes
Person C: 5 minutes
Person D: 10 minutes

So, if Person A and C crossed the bridge initially, 5 minutes would elapse,
because Person C takes 5 minutes to cross. Then, Person A would have to come
back to the other side of the bridge, taking another minute, or six minutes
total. Now, if Person A and D crossed the bridge next, it would take them 10
minutes, totaling to 16 minutes. If A came back, it would take yet another
minute, totally 17... the bridge would collapse with A and B on the wrong
side. How can all four people get across the bridge within 17 minutes? Note:
there is no trick-answer to this problem. You can't do tricky stuff like
throwing the flashlight back from one end of the bridge to the other. This
problem can be solved!
5. Container A has one liquid and Container B has another liquid:
Both are equal density and assume are completely soluble in eachother
If you take one teaspoon of B and drop into A, Then take one teaspoon of A
and drop into B. Do you have more of A in B or B in A?
6. Two doors (one leads to Goodness and one leads to Badness). We don't know which door is which. There is a man standing in front of each door. One of the men always lies and the other always tells the truth, but we don't know which. We have one question to ask either of the men. What do we ask inorder to find out which door will lead to Heaven?