# Find the different paths possible

Consider a rectangular grid of 4×3 with lower left corner named as A and upper right corner named B. Suppose that starting point is A and you can move one step up(U) or one step right(R) only. This is continued until B is reached. How many different paths from A to B possible ?

Now let’s look at some sample paths we can figure out by inspection.

If we start at A and move towards B, we find we can follow the path

RRRUU

(where R = Right one unit, U = Up one unit),

UURRR,

RURUR,

RRUUR,

and so on.

By analyzing our good routes, we see that every good route consists of 5 moves and we have 3 R moves and 2 U moves. We canuse this to generalize a formula to find the number of possible routes.

Since as we’ve shown, order does not matter in our paths (we can have an R in any place of our 5 moves), we can use our combination formula:

C(N,R) = N!/(N-R)! * R!

The number of how many good routes we have can be found by finding how many combinations of 3 R’s we can have in our 5 moves, so we want to calculate:

C(5,3) = 5!/(5-3)! * 2! = 10

### Your Answer

## More puzzles to try-

### grape vines plant riddle

What are the maximum number of grape vines that can be planted, not closer than nine feet apart, in a ...Read More »### Never finish

What work can one never finish???Read More »### Fund and Spends

I have Rs.50 and I spend it in the way as below.Read More »### City without People

What City has No People? A) Velocity B) Electricity C) Elasticity D) All the aboveRead More »### Connect circle with 6 continous straight lines

Using six contiguous straight lines, connect all of the sixteen circles shown below Hint: Think of out the boxRead More »### Hourglasses puzzle

You have two hourglasses. One measured 7 minutes and the other 11 minutes. How will you measure the 15 minutes ...Read More »### Find the Culprit

All his relatives and friends know John’s Debit Card PIN. Today John makes a profit of INR 10,000. So he ...Read More »### Count the Triangles

Can you count the triangle in below given figure ?Read More »### Which room is safest for him?

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### How can this be?

A woman shoots her husband. Then she holds him under water for over 5 minutes. Finally, she hangs him. But ...Read More »### Candies interview puzzle

In a closed jar, There are Three strawberry candies, Two mango candies and Five pineapple candies. You can’t see inside ...Read More »### Come in different shapes and sizes

I come in different shapes and sizes. Parts of me are curved, other parts are straight. You can put me ...Read More »### Animals towards city

Two Dogs saw 6 Camels while going towards City. Every Camel saw 2 monkeys are going towards city. Every monkey ...Read More »### Two Children Puzzle

I ask people at random if they have two children and also if one is a boy born on a ...Read More »### What word doesn’t belong in this group?

What word doesn’t belong in this group? That, hat, what, mat, cat, sat, pat, or chat?Read More »### Arrange 7 men in alternative height

There are 7 people numbered as 1 to 7. The number denotes their height. Arrange them in a line in ...Read More »### A Big and small person

A big person and a small person are going to market. The big person is not a small person father ...Read More »### Colourful !!!

What is red and blue, and purple and green? No one can reach it, not even the queen?Read More »### Enclosing land by fence pieces

You are given one 44-meter piece of fence and 48 one-meter pieces of fence. Assume each piece is a straight ...Read More »### Meteor Shower

Can you protect the planets from the meteor shower? Draw nine straight lines through the box below to separate the ...Read More »