There are six numbers which are not divisible by 6

[rajesh]

There are six numbers which are not divisible by 6.
Prove that there are atleast two numbers in this set such that the difference between them is divisible by 6.

 

[matt grime]

pigeon hole principle.

their are six remainders possible on division by 6. none of the numbers in your set has remainder zero so two of them must be...

 

[Alkatran]

There are six numbers which are not divisible by 6.
Prove that there are atleast two numbers in this set such that the difference between them is divisible by 6.

Let's say x is our set of six values
x mod 6 <> 0 so:
x mod 6 = 1 and 2 and 3 and 4 and 5 and y

y being the sixth value.

We also know that y <> 1 <> 2 <> 3 <> 4 <> 5 <> 0
y is not contained within the range of n mod 6.

so...

 

[rajesh]

i didnt get both of u...
please elaborate

 

[T@P]

do you know what the pidgeon hole prinicipal is? if you dont, it states (sort of obvious) that if you have x holes and x + 1 pidgeons and all pidgeons go to some hole, there will be one hole with at least 2 pidgeons. Applied to the problem, i think matt grime was basically show that there are only 5 possible remainders if a number is not divisible by 6, and then he just enumerated the possibilities. Is that right Matt grime?

 

[matt grime]

Look up the pigeon hole principle and the idea of remainder or modulo arithmetic. We won't do all the work for you

 

[rajesh]

got it...thanks