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.
Fariha had an apple.
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!!!
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
More puzzles to try-
- A runner timed himself and found out that if he wore a white outfit he ran 10 miles in 70 ...Read More »
- Who can jump higher than a mountain?Read More »
- A number can be multiplied by multiple of nine i.e 9 18 27 36 45 … and the resulting number ...Read More »
- Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is ...Read More »
- Can you transform the word THINK into BRAIN while changing only one letter at a time in a manner that ...Read More »
- A man in New York City has $10. He spends $6.50 on flowers, and $3 on lunch (hot coffee and ...Read More »
- The more we take, the more we leave behind. What is it?Read More »
- Role Action Block Prevents the target player from acting Redirect Change target player target. Save Protects the target player from ...Read More »
- Use digits from 1 to 9 once in such a way that each digit is used in the boxes and ...Read More »
- In a class test the rank of five students are: Joe did not come second Julie did not come first ...Read More »
- You have a normal six sided cube. I give you six different colors that you can paint each side of ...Read More »
- Can you find out how many prime numbers that are less than 95 will leave an odd reminder when divided ...Read More »
- Can you make a six-letter word using the letters N, A and B ?Read More »
- A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by ...Read More »
- Three college toppers are summoned by the inspecting faculty. To identify the best from them, the faculty takes them into ...Read More »
- Your sock drawer contains ten pairs of white socks and ten pairs of black socks. If you’re only allowed to ...Read More »
- 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, accused of high disloyalty, is sentenced to death by the court-martial. He is allowed to make a final ...Read More »
- You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. ...Read More »
- While walking down the street, one morning, I found a hundred rupee note on the footpath. I picked it up, ...Read More »