### #1 - Sherlock Holmes Puzzle

Sherlock Detective reviewed the information they had on the case so far.

A lady named 'himanshi' was found shot and they already had a list of suspects - Ankit , Tarun, Harish, Manoj and Manish.
Killer is a fan of sherlock and chalenge him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at anyplace the notes were.
Sherlock the genius , immediately solved the case.
Who was the killer ?

Its Tarun

toilet room(T) , art room(a) , rest room (r) , underwater room (u) , no smoking room (n)

### #2 - Awesome Word Changing Riddle

Can you transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word?

THINK

Replacing N with C
THICK

Replacing H with R
TRICK

Replacing I with A
TRACK

Replacing K with T
TRACT

Replacing C with I
TRAIT

Replacing T with N
TRAIN

Replacing T with B
BRAIN

### #3 - Difficult Brain Twister

There are 100 bulbs in a room. 100 strangers have been accumulated in the adjacent room. The first one goes and lights up every bulb. The second one goes and switches off all the even numbered bulbs - second, fourth, sixth... and so on. The third one goes and reverses the current position of every third bulb (third, sixth, ninth… and so on.) i.e. if the bulb is lit, he switches it off and if the bulb is off, he switches it on. All the 100 strangers progresses in the similar fashion.

After the last person has done what he wanted, which bulbs will be lit and which ones will be switched off ?

Ponder over the bulb number 56, people will visit it for every divisor it has. So 56 has 1 & 56, 2 & 28, 4 & 14, 7 & 8. So on pass 1, the 1st person will light the bulb; pass 2, 2nd one will switch it off; pass 4, light it; pass 7, switch it off; pass 8, light it; pass 14, switch it off; pass 28, light it; pass 56, switch it off.
For each pair of divisors the bulb will just end up back in its preliminary state. But there are cases in which the pair of divisor has similar number for example bulb number 16. 16 has the divisors 1 & 16, 2 & 8, 4&4. But 4 is recurring because 16 is a perfect square, so you will only visit bulb number 16, on pass 1, 2, 4, 8 and 16… leaving it lit at the end. So only perfect square bulbs will be lit at the end.

### #4 - Ramanujan Magic Number Riddle

Ramanujan discovered 1729 as a magic number.

Why 1729 is a magic number ?

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

### #5 - Hard Logic Puzzle

A gardener planted the mangoes trees in a mathematical ordered way (i.e. he planted tree in rows).
He created total of 19 rows of trees.

Note: There should be more than 2 trees to count as a row.

What is the minimum number of trees required by the gardener to have 19 rows of trees ?

A B C
E F G H
I J K L
M N O P
R S T
5 horizontal rows
4 vertical columns
4 diagonals with slope 1 (ROL, NKH, MJG, IFC)
4 diagonals with slope -1 (SNI, TOJE, PKFA, LGB)
2 knight's move diagonals with slope -2 (AJS, BKT)

### #6 - Tough next number sequence

Find the next number in the sequence 23 21 24 19 26 15 28 11 30 7 36 ?

5

23-2=21
21+3=24
24-5=19
19+7=26
26-11=15
15+13=28
28-17=11
11+19=30
30-23=7
7+29=36
36-31=5

(2,3,5,7,11,13,17,19,23,29,31,37,41,43... are Prime Numbers)

### #7 - Hard Pattern Puzzle

In which direction should the missing arrow point ?

South
The series: south, east, north, south, west, east spirals clockwise from the top left-hand corner.

### #8 - Albert Einstein Cipher Puzzle

Can you decipher these quotes by Albert Einstein?
Blf xzm mvevi hloev z kilyovn lm gsv ovevo lm dsrxs rg dzh xivzgvw.

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

### #9 - Decode This Message

Decode The Message

carrot fiasco nephew spring rabbit
sonata tailor bureau legacy corona
travel bikini object happen soften
report accuse animal shriek esteem
oyster

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

### #10 - Hardest Mathematical Columbus Puzzle

The Puzzle: Here is a famous prize problem that Sam Loyd issued in 1882, offering \$1000 as a prize for the best answer showing how to arrange the seven figures and the eight 'dots' .4.5.6.7.8.9.0. which would add up to 82

The dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc)
With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc)
The remarkable feature being that a proper fraction divided by 9s e.g. 46/99 is exactly equal to the numerator with the repeater sign followed by the decimal.