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-
Vampires biting puzzle
A vampire enters a town and bites 2 person every night. The bitten 2 persons grows in to two big ...Read More »Complex Relational Puzzle
Alex is father of B and Duke is son of C. Enrique is brother of A and E also has ...Read More »Number Of Races Puzzle
In order to complete the racing competition, the London racetrack has to submit its top and the most famous three ...Read More »Who Are These People ?
The first person saw the bridge step on it and crossed, the second person saw the bridge did not step ...Read More »Change Gender and Number
I am looking for a word that change both gender and number when i add the letter ‘S’. What Word ...Read More »what do you open first?
You are awoken at 3 A.M. by a knock on your door. Your parents call you to let you know ...Read More »Hide and Seek
A farmer was playing hide and seek with his wife. His wife hid in their family’s vehicle. How did the ...Read More »Digging Tiny Caves
He dig out tiny caves, and store gold and silver in them. He also build bridges of silver and make ...Read More »Cricket Ball Puzzle
At Delhi Cricket Clubhouse, there were four kids(Kohli, Yuvraj, Pant, and Dhoni) ages 1,2,3 and 4 and have 1,2,3 and ...Read More »Which is the Top View Puzzle
Find out which of the given views in the picture is the top view of the given pyramid.Read More »Game of Cards
13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from ...Read More »Next Number?
Find The Next Number in the series: 12 13 15 17 111 113 117 119 123 ?Read More »What’s the mother’s name?
A dog had three Puppies: January,March and May. What was the mother’s name. What’s the mother’s name? Think think What’s the ...Read More »Prime Number Puzzle
It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten-digit numbers. But ...Read More »Business trek with their respective wives and crossing the river puzzle
Three jealous personnel at IGHALO Ltd went on a business trek with their respective wives and they needed to cross ...Read More »Can you make expressions to make 100 using 9’s and operators?
You have four 9’s and you may use any of the (+, -, /, *,.) as many times as you like. ...Read More »Common Names
What do the following words have in common? Vermont, Statuesque, Swedish, Arthur\’s, Africa, Sensation, Misunderstood?Read More »Pattern Forecast
What is represented by this BrainBat Pattern? EST EST EST ESTRead More »Letter for Maths
If, A = 1 B = 2 C = 3 … … Z = 26. Based on above rule, you ...Read More »Treasure in gold and silver pot puzzle
There is a silver pot and a golden pot. One of these pots contains a treasure and the other one ...Read More »
