Digit Column Route

M2007U-E2016-A2017-S2017-Mat_SMT-28Mar2017-1

Setup

Pick any number from 1 to 9, and call it the factor F.

Arrange the numbers 1 to 9 into a table/matrix, from the left to right, bottom to top.

Then add the number "0" to a new row at the bottom of the matrix and aligned to the last column.

Feature

for the multiples of the Factor F which are smaller than 99,

the numbers of Tens which are inside a certain column in the matrix will point to the numbers of Ones which are inside a certain column in the matrix as well.

Resulting in certain columns will always "point to" a certain column, and the last column will always point to itself.

Example

Let's say we pick the number 3 as our Factor F

then the multiples would be:

03, 06, 09, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54...

for "03", Tens is "0" in column3, Ones is "3" in column3, (col3→col3)

for "06", Tens is "0" in column3, Ones is "6" in column3, (col3→col3)

for "24", Tens is "2" in column2, Ones is "4" in column1, (col2→col1)

for "57", Tens is "5" in column2, Ones is "7" in column1, (col2→col1)

for "15", Tens is "1" in column1, Ones is "5" in column2, (col1→col2)

for "48", Tens is "4" in column1, Ones is "8" in column2, (col1→col2)

and so on...

in this case, the result would be:

when Factor is 3,

column 1 points to column 2

column 2 points to column 1

column 3 points to column 3

Do you know?

This discovery is inspired by staring at a calculator long enough because the number keys are arranged in a 3x3 matrix with a 0 at a new row but aligned on the left side.