Solution:

After analyzing the possibilities, it is obvious that my friend has better chances of winning and his average score will be lower at the end.

Let us assume that we have not completed the sequence yet and understand the possibilities. If the last toss of coin was tails, start with step 1 otherwise start at step 2.

Step 1: If either of us toss the coin to get tails, nothing will change. We both will still be at step one and we both will still be needing three more correct tosses of coin to complete our respective sequences. If we get heads, then we continue.

Step 2: If either of us tosses the coin to get heads, we stay on this very step. If we get tails, we continue.

Step 3a (me): If I tosses the coin to get tails, I will have to go back to the step one again and try till I get heads again. Thus I will need at least 3 more tosses to complete my sequence.

Step 3b (my friend): If my friend tosses the coin to get heads, he will go back to step 2 again and will try till he gets tails. In this scenario, he will need at least 2 more tosses to complete the sequence.

Clearly, he has the better opportunity to win this game.

Solution:

The figure comprises of 92 triangles.

Solution:

11550

Explanation:
There is just one way to find it out and that is the generic computing method.

The number of squares and rectangles formed = (Summation of column numbers)
= (1 + 2 + 3 +......+ 19 + 20) * (1 + 2 + 3 +......+ 9 + 10)
= 210 * 55
= 11550

Solution:

THINK

Change N to C
THICK

Change H to R
TRICK

Change I to A
TRACK

Change K to T
TRACT

Change C to I
TRAIT

Change T to N
TRAIN

Change T to B
BRAIN

Solution:

megalomaniac.

Camel (2, 4, 7, 2, 5 are Eastern beast of burden)
Main (1, 8, 10, 9 are street made famous by Sinclair Lewis)
Ago (11, 3, 6 are past)

Solution:

151 (131+20)

Explanation:
1st 7 prime numbers post 100 are
101 , 103 , 107 , 109 , 113 , 127 , 131
...Adding 20 to numbers
121 , 123 , 127 , 129 , 133 , 147 , 151

Solution:

"EUNOIA" is the shortest(length-6) word that comprises of all vowels.
But many dictionaries does no include this word.

So next comes many seven letter words that contain all vowels.
* SEQUOIA,
* EULOGIA,
* MIAOUED,
* ADOULIE,
* EUDOSIA,
* EUNOMIA
* EUTOPIA
* MOINEAU
* DOULEIA.

EUNOIA means "alertness of brain"

Solution:

89

Solution:

Amin is the terrorist

Explanation:
The message is "tstimeirorwatchretehourhtsisecondsnidialma"

Step1 :
Rewrite the above message as
"ts time iror watch rete hour htsi seconds ni dial m"

Step2:
Now remove all words related to time like (time,watch,hour,seconds,dial) and combine them.
"tsirorretehtsinima"

Step3
Reverse the word.
"tsirorretehtsinima"

Step4.
Add spaces where necessary
"tsirorret eht si nima"

Step5:
Reverse again
"amin is the terrorist"

Solution:

Image C

Explanation:
If we add one matchstick to any other image, it forms a full-length capital letter.