Question

six consecutive numbers are each divided by 6 and their remainders are recorded , what is sum of their reaminders

Answer 1

Explanation:

Six consecutive integers are:

x,x+1,x+2,x+3,x+4,x+5,

Hence,sum of their remainders are 1+2+3+4+5=15

Answer 2

Note that for any integer
`k`,


`n\equiv\begin{cases}0\mod6&\text{if }n=6k\\1\mod6&\text{if }n=6k+1\\2\mod6&\text{if }n=6k+2\\3\mod6&\text{if }n=6k+3\\4\mod6&\text{if }n=6k+4\\5\mod6&\text{if }n=6k+5\end{cases}`

and if
`n=6k+6=6(k+1)`, well
`n` is just another multiple of 6, so we're back to the first case.

For any six consecutive integers, then, the sum of the remainders upon division by 6 is
`0+1+2+3+4+5=15`.