# (Puzzles) Challenging Mathematical Puzzles (31)

**Puzzles : Challenging Mathematical Puzzles**

**101. You have four 9's and you may use any of the (+, -, /, *) as many times as you like. I want to see a mathematical expression which uses the four 9's to = 100.
How many such expressions can you make?**

**Answer : -**

__There are 5 such expressions.__

99 + (9/9) = 100

(99/.99) = 100

(9/.9) * (9/.9) = 100

((9*9) + 9)/.9 = 100

(99-9)/.9 = 100

**102. 12 members were present at a board meeting. Each member shook hands with all of the other members before & after the meeting.
How many hand shakes were there?
Answer : -** 132

Think of it this way: the first person shakes hands with 11 people, the second person also shakes hands with 11 people, but you only count 10, because the hand shake with the first person was already counted. Then add 9 for the third person, 8 for the fourth, & so on.

66 hand shakes took place before & 66 after the meeting, for a total of 132.

**103. Arrange five planets such that 4 of them add up to 5th planet numerically. Each of the letters of the planet should represent a unique number from the range 0 - 9. You have to use all ten digits.
There is an amazing mathematical relationship exists among the names of the planet.
Answer : -**

The tought process is initially to find planets such that the total number of alphabets in them is 10.

The only possible combination of planets is Saturn, Uranus, Venus, Mars and Neptune because for other combinations there will be more than 10 alphabets. Among these five, Neptune is the lenghtiest, so it must be the sum of the other four.

S A T U R N

U R A N U S

V E N U S

+ M A R S

--------------

N E P T U N E

Now the only possible value for N is 1. By finding the value for S, we can reach the result:

3 5 8 6 9 1

6 9 5 1 6 3

2 0 1 6 3

+ 4 5 9 3

--------------

1 0 7 8 6 1 0

**104. You have 14 apples. Your Friend Marge takes away 3 and gives you 2. You drop 7 but pick up 4. Bret takes 4 and gives 5. You take one from Marge and give it to Bret in exchange for 3 more. You give those 3 to Marge and she gives you an apple and an orange. Frank comes and takes the apple Marge gave you and gives you a pear. You give the pear to Bret in exchange for an apple. Frank then takes an apple from Marge, gives it to Bret for an orange, gives you the orange for an apple.
How many pears do you have?
Answer :- **None

Frank gave you a pear in exchange of the apple which Marge gave you. And you gave that pear to Bret in exchange for an apple. All the others exchanges involved apples and/or oranges.

105. Four couples are going to the movie. Each row holds eight seats. Betty and Jim don't want to sit next to Alice and Tom. Alice and Tom don't want to sit next to Gertrude and Bill. On the otherhand, Sally and Bob don't want to sit next to Betty and Jim.

How can the couples arrange themselves in a row so that they all sit where they would like?

Answer :-

From the given data, it can be inferred that:

(Sally & Bob) NOT (Betty & Jim) NOT (Alice & Tom) NOT (Gertrude & Bill)

(A) NOT (B) means A and B can not seat next to each other.

Now, it is obvious that (Betty & Jim) and (Alice & Tom) will occupy the corner seats as both of them can have only one neighbour. Therefore,

(Gertrude & Bill) will seat next to (Betty & Jim)

(Sally & Bob) will seat next to (Gertrude & Bill)

(Alice & Tom) will seat next to (Sally & Bob)

Thus, there are two possible arrangements - a mirror images of each other.

1. (Betty & Jim) - (Gertrude & Bill) - (Sally & Bob) - (Alice & Tom)

2. (Alice & Tom) - (Sally & Bob) - (Gertrude & Bill) - (Betty & Jim)

**106. Substitute digits for the letters to make the following addition problem true.
W H O S E
T E E T H
A R E
+ A S
------------------
S W O R D S
Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter H, no other letter can be 3 and all other H in the puzzle must be 3.
Answer : - **

It is obvious that S=1 and T=9.

Also, (H + E) should be greater than 10 and hence, (E + H + E) must 20. Thus, there are 3 possible values for (E, H) pair: (6, 8) or (7, 6) or (8, 4). Use trial-n-error and everything will fit-in.

W H O S E 2 8 5 1 6

T E E T H 9 6 6 9 8

A R E 4 7 6

+ A S + 4 1

------------------ -------------------

S W O R D S 1 2 5 7 3 1