Solution:

Batsman-8

1st over:
1st Ball, Batsman-1 got out
2nd Ball, Batsman-3 got out
3rd Ball, Batsman-4 got out
4th Ball, Batsman-5 got out
5th Ball, Batsman-6 got out
6th Ball, Batsman-7 got out

Before the start of a new over, the batsmen will swap strikes.
i.e Batsman-2 at nonstriker will become striker and batsman-8 will go at the nonstriker end.

2nd over:
1st Ball, Batsman-2 got out
2nd Ball, Batsman-9 got out
3rd Ball, Batsman-10 got out
4th Ball, Batsman-11 got out.

Solution:

So, for 100 tigers to catch 100 sheep, it would still take the same amount of time because each tiger is catching one sheep in 3 minutes. Therefore, it would take 3 minutes for 100 tigers to catch 100 sheep.

Solution:

he was genius.

Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute.

Solution:

138,150,180

The series lists numbers that are flanked by two prime numbers.

4 (3 and 5 are prime)
6 (5 and 7 are prime)
12 (11 and 13 are prime)
18 (17 and 19 are prime)
30 (29 and 31 are prime)
42 (41 and 43 are prime)
60 (59 and 61 are prime)
72 (71 and 73 are prime)
102 (101 and 103 are prime)
108 (107 and 109 are prime)

thus

138 (137 and 139 are prime), 150 (149 and 151 are prime), 180 (179 and 181 are prime)

Solution:

10 prisoners must sample the wine. Bonus points if you worked out a way to ensure than no more than 8 prisoners die.

Number all bottles using binary digits. Assign each prisoner to one of the binary flags. Prisoners must take a sip from each bottle where their binary flag is set.

Here is how you would find one poisoned bottle out of eight total bottles of wine.

Bottle 1 Bottle 2 Bottle 3 Bottle 4 Bottle 5 Bottle 6 Bottle 7 Bottle 8
Prisoner A X X X X
Prisoner B X X X X
Prisoner C X X X X
In the above example, if all prisoners die, bottle 8 is bad. If none die, bottle 1 is bad. If A & B dies, bottle 4 is bad.

With ten people there are 1024 unique combination so you could test up to 1024 bottles of wine.

Each of the ten prisoners will take a small sip from about 500 bottles. Each sip should take no longer than 30 seconds and should be a very small amount. Small sips not only leave more wine for guests. Small sips also avoid death by alcohol poisoning. As long as each prisoner is administered about a milliliter from each bottle, they will only consume the equivalent of about one bottle of wine each.

Each prisoner will have at least a fifty percent chance of living. There is only one binary combination where all prisoners must sip from the wine. If there are ten prisoners then there are ten more combination where all but one prisoner must sip from the wine. By avoiding these two types of combination you can ensure no more than 8 prisoners die.

One viewer felt that this solution was in flagrant contempt of restaurant etiquette. The emperor paid for this wine, so there should be no need to prove to the guests that wine is the same as the label. I am not even sure if ancient wine even came with labels affixed. However, it is true that after leaving the wine open for a day, that this medieval wine will taste more like vinegar than it ever did. C'est la vie.

Solution:

Starting with the first two words, Take the first and last letters, reading from left to right. Example: Carrot fiascO "from these pairs" the message is as follows:

CONGRATULATIONS CODE BREAKER

Solution:

You can never solve a problem on the level on which it was created.

Here is the answer key:
A-Z
B-Y
C-X
D-W
E-V
F-U
G-T
H-S
I-R
J-Q
K-P
L-O
M-N
N-M
O-L
P-K
Q-J
R-I
S-H
T-G
U-F
V-E
W-D
X-C
Y-B
Z-A

Solution:

Bill. If you read the message upside down, you'll notice that the numbers resemble letters and that those letters form legible sentences. The message is 'Bill is boss. He sells oil.'

Solution:

prinka is 10, in a system that awards five for each vowel.

Solution:

They can be expressed as the sum of the cubes of two different sets of numbers.

10^3 + 9^3 = 1729
and
12^3 + 1^3 = 1729