what's something unusual about the numbers 45 and 2025 ?

number 45 is special ~ a Kaprekar number !

The first few are 1, 9, 45, 55, 99, 297, 703, ... (Sloane's A006886).

 

45^2 = 2025  and  20 + 25 = 45

 

2025 = ( 20 + 25 ) * 45

the visualisation below shows the 2025 small unit squares

in two different ways

as a  5*9  arrangement of components
each having  9*5  unit square dimensions

or a  9*5  arrangement of components
each having  5*9  unit square dimensions

 

 

odd~one~out

and I thought about 2025 as 100*20 + 25

how many ways to place the unit black squares within the rectangles ? 

 

 

... the answer is

( 20^100 ) * 25 =

316912650057057350374175801344000000
00000000000000000000000000000000

00000000000000000000000000000000
00000000000000000000000000000000