Solution:

answer is: 14

Let x be the answer we want, the number of drops required.

So if the first egg breaks maximum we can have x-1 drops and so we must always put the first egg from height x. So we have determined that for a given x we must drop the first ball from x height. And now if the first drop of the first egg doesn’t breaks we can have x-2 drops for the second egg if the first egg breaks in the second drop.

Taking an example, lets say 16 is my answer. That I need 16 drops to find out the answer. Lets see whether we can find out the height in 16 drops. First we drop from height 16,and if it breaks we try all floors from 1 to 15.If the egg don’t break then we have left 15 drops, so we will drop it from 16+15+1 =32nd floor. The reason being if it breaks at 32nd floor we can try all the floors from 17 to 31 in 14 drops (total of 16 drops). Now if it did not break then we have left 13 drops. and we can figure out whether we can find out whether we can figure out the floor in 16 drops.

Lets take the case with 16 as the answer

1 + 15 16 if breaks at 16 checks from 1 to 15 in 15 drops
1 + 14 31 if breaks at 31 checks from 17 to 30 in 14 drops
1 + 13 45 .....
1 + 12 58
1 + 11 70
1 + 10 81
1 + 9 91
1 + 8 100 We can easily do in the end as we have enough drops to accomplish the task


Now finding out the optimal one we can see that we could have done it in either 15 or 14 drops only but how can we find the optimal one. From the above table we can see that the optimal one will be needing 0 linear trials in the last step.

So we could write it as

(1+p) + (1+(p-1))+ (1+(p-2)) + .........+ (1+0) >= 100.

Let 1+p=q which is the answer we are looking for

q (q+1)/2 >=100

Solving for 100 you get q=14.
So the answer is: 14
Drop first orb from floors 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, 100... (i.e. move up 14 then 13, then 12 floors, etc) until it breaks (or doesn't at 100)

Solution:

Wristwatches

Most of us must have assumed the answer to be a ring in the wrong finger but that's not the case as it's a normal ring. The error is in the watch. Wristwatches are manufactured with the adjustment pin always on the right side.

Solution:

7

Explanation:
Put batteries into 3 groups: two groups of 3 and one group of 2.
It guarantees at least one of the group has got two working battery
Group of 3 requires 3 attempts to verify if 2 batteries of the group are working (B1+B2, B2+B3, and B1+B3) while the group of 2 requires one attempt (B1+B2)
Total attempts = 3 + 3 + 1 = 7

Solution:

8 Steps

Explanation:
Steps------2L Gallon-------5L Gallon
A-------------12-------------0
B-------------07-------------5
C-------------07-------------0
D-------------02-------------5
E-------------02-------------0
F-------------00-------------2
G-------------12-------------2
H-------------09-------------5

Solution:

7 Trips

Explanation:
Send 2+5+9 = 16
Bring back 9
Send 3+4+9 = 16
Bring back 9
Send 1+7+8 = 16
Bring back 1
Send 1+6+9 = 16

Solution:

Pour 3 lumps on cup-1 and cup-3 and 4lumps on cup4 and place them as shown in the picture.

Explanation:
Now,
Cup-1 got three sugar lumps
Cup-3 got three sugar lumps
Cup-2 got three seven lumps (3 of cup-1 and 4 of its own)

Solution:

Federer serves first

Explanation:
The one who serves first can serve 5 and other will serve four.

== Option A ==
If Federer serve 4 and Nadal serve 5
Then five service breaks and Federer winning 6:3 not possible.

== Option B ==
Federer serve 5 and Nadal serve 4
There are five service breaks and score is Federer 6 - Nadal 3
i.e
On Federer serve, Federer wins 3 and lost 2
On Nadal serve, Federer wins 3 and lost 1

Solution:

Rashid's son-1: 1 11 21 31 41 51 61 71 81
Rashid's son-2: 2 12 22 32 42 52 62 72 73
Rashid's son-3: 3 13 23 33 43 53 63 64 74
Rashid's son-4: 4 14 24 34 44 54 55 65 75
Rashid's son-5: 5 15 25 35 45 46 56 66 76
Rashid's son-6: 6 16 26 36 37 47 57 67 77
Rashid's son-7: 7 17 27 28 38 48 58 58 78
Rashid's son-8: 8 18 19 29 39 49 59 69 79
Rashid's son-9: 9 10 20 30 40 50 60 70 80

Solution:

Day 1:
Alibaba Give 1kg gold bar.

Day2:
Now Alibaba gives 2kg gold bar and takes back 1kg gold bar back.

Day3:
Alibaba gives 1kg gold bar.

Day4:
Alibaba gives 4kg gold bar and take back 1kg gold bar back

Day5:
Alibaba gives 1kg gold bar.

Day6:
Alibaba gives 2kg gold bar and takes back 1kg gold bar back.

Day7:
Alibaba gives 1kg gold bar.

Solution:

The code is 645
Explanation :
A) From Clues 1st and 2nd we know that one 9 is not in the code
B) From Clue 2nd we know that 9 3 and 8 are part of code
C) From Clue 3rd we know that 4 and 6 are part of code
D) From Clue 5th we know that 1 and 2 are not part of the code as we know 6 is part of the code and just 1 of 3 numbers is part of code.
E) From Clue 4th we know that 5 is also in the code as 8 and 1 are not part of code.

So the code is: 645