My little brother's challenge for you!

Number Theory Level 3

Let's write every natural number $n>1$ in form of a table as below:

Based on the table, in what column would the number 2015 appear?

\text{B}

\text{A}

\text{E}

\text{D}

\text{C}

1 solution

Leah Smith
Sep 18, 2015

There are quite a few solutions to this problem, but here is my brother's:

We can easily see that the numbers on column a, c, e are even number . Let n be any natural numbers, we can figure out that:

○ Every number in column a represents 8n + 2 .

○ Every number in column c represents 4n .

○ Every number in column e represents 8n + 6 .

2014 = 8*251 + 6, so it would be written in column e .

2016 = 4*504, so it would be written in column c .

Hence, 2015 would be written in column d

To put it differently: The multiples of 8, like $8,16,..,2016,..$ are in column C, and their predecessors, like $7,15,..2015,..$ , are in column D.

Otto Bretscher - 5 years, 8 months ago