# Fariha’s Game

1,022.2K Views

Fariha invented a game!
In that game, Fariha kept 5 plates on a circular dining table!
The plates were marked as 1,2,3,4,5.
On the first move, she put that apple to the clockwise neighboring plate no 2 from plate no 1.
On the second move, she moved the apple from no 2 table to no 4 table.
So on her kth move she actually moved the apple for k positions!
And after some moves she reached the plate no 1 again.
Now her friend Nabila put some more plates on the table.
Now could Fariha find out if it was possible for her to reach plate no 1 again after any number of moves!!!

thesucker Expert Asked on 7th June 2016 in

the apple is moving in this way : (1+2+3+4+….)
so if the sum of (1+2+3+4+5+…) is divisible by the number of plates then the apple will reach the plate no 1

namrata Starter Answered on 9th June 2016.

1 then 2 then 3 then 4 then 5 etc (how  moves go)
so position  of apple will be like,1,1+2,1+2+3,1+2+3+4,as every move goes (position from first plate)
so if we divide total by number of plates remainder will tell the position of apple at end .since sum  can be formalised into n(n+1)/2 where n is last value  of series .so the number of plates must be factor of n(n+1)/2 if we want it to end in first place.
so if number of plates is k then if i choose n=k square.(k^2)  so it will be.k^2(k^2 +1)/2 should be divisible by k and  it is divisible by k so it will always happen no matter how many plates it is always possible

Yodha Expert Answered on 9th June 2016.

• ## More puzzles to try-

• ### Runner outfit

A runner timed himself and found out that if he wore a white outfit he ran 10 miles in 70 ...Read More »
• ### Jump higher than mountain puzzle

Who can jump higher than a mountain?Read More »
• ### Maths Magic

A number can be multiplied by multiple of nine i.e 9 18 27 36 45 … and the resulting number ...Read More »
• ### Disk colour riddle

Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is ...Read More »
• ### Word Change Riddle

Can you transform the word THINK into BRAIN while changing only one letter at a time in a manner that ...Read More »
• ### Tricky calculation

A man in New York City has \$10. He spends \$6.50 on flowers, and \$3 on lunch (hot coffee and ...Read More »
• ### Take and Leave behind riddle

The more we take, the more we leave behind. What is it?Read More »
• ### Who is the murderer?

Role Action Block Prevents the target player from acting Redirect Change target player target. Save Protects the target player from ...Read More »
• ### 1 to 9 all digits to be used puzzle

Use digits from 1 to 9 once in such a way that each digit is used in the boxes and ...Read More »
• ### Ranking The Students

In a class test the rank of five students are: Joe did not come second Julie did not come first ...Read More »
• ### Cube Puzzle

You have a normal six sided cube. I give you six different colors that you can paint each side of ...Read More »
• ### Prime number divided by 5 puzzle

Can you find out how many prime numbers that are less than 95 will leave an odd reminder when divided ...Read More »
• ### Word made of 3 Letters

Can you make a six-letter word using the letters N, A and B ?Read More »
• ### Choose the Dress

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by ...Read More »
• ### Most Intelligent Student

Three college toppers are summoned by the inspecting faculty. To identify the best from them, the faculty takes them into ...Read More »
• ### Minimum chances to draw a pair of same color

Your sock drawer contains ten pairs of white socks and ten pairs of black socks. If you’re only allowed to ...Read More »
• ### Horse goes to park riddle

If Wednesday the horse goes into the park at 6:00 and on Saturday the horse goes into the park at ...Read More »
• ### Army General Word riddle

Army General, accused of high disloyalty, is sentenced to death by the court-martial. He is allowed to make a final ...Read More »
• ### FIND THE RIGHT DOOR

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. ...Read More »
• ### Find the missing amount

While walking down the street, one morning, I found a hundred rupee note on the footpath. I picked it up, ...Read More »