# 1089

Choose a 3 digit number whose first and last digits differ by at least 2.

E.g 853

Reverse this number

I.e. 358

Subtract the smaller from the larger

I.e. 853 – 358 = 495

Add this number to the reverse of this number

I.e. 495 + 594 = 1089

Why? (That’s the fascinating part of maths.)

Thanks to Alex Bellos’s book “Alex’s Adventures in Numberland” for rekindling my interest in numbers.

My demonstration of why 1089 is the answer:

 hundreds tens units notes start a b c a>c+1 invert c b a subtract a-(c+1) 10+b-(b+1) 10+c-a +10 carry 1 in tens,units simplify 9 invert 10+c-a 9 a-(c+1) add 10 8 9 Carry 1 in tens

## 4 thoughts on “1089”

1. i love stuff like this; my eighth grade math teacher showed me the magic of nine, and I’ve been playing ever since. he was a dreadful teacher who loved math but just couldn’t teach it. Poor soul.

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2. I’ve seen proofs of this using number theory though they are quite long, considering that this can be easily proven using basic algebra.

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• Yes it is easily demonstrated using basic algebra, but appears magical if you don’t know algebra.

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• Harry Lorayne’s book Mathematical Wizardry gives several applications of the 1089 trick and he made them more magical. Also, the other tricks included in the book are very amazing as well. The paperback version is quite expensive though, so I just bought the e version from his site.

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