Table of integers
Is it possible to arrange infinite number of integers in the form of a table
(like a chessboard), so that every integer is the average of the 8 integers surrounding it?
Yes it is possible
a=b+c
b=d+e
c=f+g
d=h+i
e=j+k
f=l+m
g=n+o
Now suppose a is a middle number in 3 by 3 box
since any integer can be expressed as sum of two integers with infinite possibilities .following the above steps we can understand a can be expressed as sum of h,I,j,k,l,m,n,o .with each variable having infinite possibiles.now at any point we can find infinite integers which can surround a satisfying given condition.this can be used for any number in the table.we will find 8 integers which we have not used .now expanding table we will never be restricted to choose one number for the numbers surrounding the boundaries of table there will at least be a option of choosing 2 now since we have used limited numbers till now.there will be numbers having a required sum and uncommon with numbers we have used.so there will be no blockage in expanding our table
Your Answer
More puzzles to try-
Two men in one riddle
I make two people out of one. What am I?Read More »Simple Riddle Of Knockout Matches
Let us say that a table tennis tournament was going on with knock out terms which means the one who ...Read More »One means None
If you have three you have three, if you have two you have two and if you have one you ...Read More »Delivery Incentive
John was a very careless driver, so his owner Jacob gave him an offer that he will get an incentive ...Read More »Classic Barber Brain Teaser
There are two barber shops in a small town – one located in the eastern market and the other in ...Read More »Word become mother
A word of three letters spelt the same backwards and forwards. Turn it upside down, will become one’s mother. What ...Read More »Counting Error Puzzle, Can you help Mrs. Alka?
Mr. Sameer a very clever person, he wanted to cheat restaurant owner Mrs. Alka by proving she have calculated his ...Read More »Sum of Product is me
When I get multiplied by any number, the sum of the figures in the product is always me. What am ...Read More »Water stop running down hill
When will water stop running down hill?Read More »Chains Puzzle
You have five pieces of chain, each consisting of three links. You want to make one long chain of these ...Read More »Light and gift riddle
People go round and round me Adding some lights on a string And later underneath me They place the gifts ...Read More »Six Letters
I am six letters. When you take one away I am twelve. What am I?Read More »Can you start the fire?
Can you start the fire using two pieces of wood?Read More »Still makes a meaningful word riddle
What an eight letter word can have a letter taken away which still makes a meaningful word. Take another letter ...Read More »Find the profit
A friend of mine bought a used pressure cooker for Rs. 60. She somehow did not find it useful and ...Read More »Has legs but does not walk
What has two legs but does not walk?Read More »What is the least number of eggs he needs for this to be true?
John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to ...Read More »What killed him?
A man was going to bleach his socks because they had gotten muddy the day before. As he was pouring ...Read More »Prime Number Puzzle
Check out the number list below and find what number comes next in the sequence. 111 , 113 , 117 ...Read More »Helpless Man
In his own home, a man watches as a woman dies, He cries, but does nothing to save her. Why ...Read More »