The number 1089

If you write a number with 3 digits without being palindrome, and if then you change the order of the digits (ABC → CBA). Now we have the number ABC and CBA, so we make a subtract of the smallest to the biggest one, having a result (DEF).  And now if we make the same thing changing the order we will get FED, and if then we make a sum of DEF and FED you will get always the same result.

1089

This could sound strange and also impossible, but it’s mathematics. Try it. You will always get 1089.

Now I will explain you why is this possible.

When we take the first number (ABC) we are taking 100A + 10B + C.

(A is the cents, B is the tens and C is the units)

Then we have to change the order, ABC → CBA, and then we have 2 numbers, so we have to make a subtraction of the smallest to the biggest one, subtracting these two numbers we get 100 (AC) +10 (BB) + CA = 100 (AC) + CA. Having assumed that A> C, obviously must be C <A,0 we have to add and subtract 100 units so the result won’t change: 100(A-C-1) +90+(10+C-A).

We can verify that this number always has the 9 in the tens position and also the sum of the first and the third number (AC-1 +10 + C + A) is also 9.

And also if we now change between them the first row and the third one and we make an addition we have this result:

100(A-C-1)+90+(10+C-A)+100(10+C-A)+90+(A-C-1)= 100A-100C-100+90+10+C-A+1000+100C-100A+90+A-C-1=1089